Browse Algebra problems in the Studdy Learning Bank!

Problem 4101

Let $x$ be the number of residents unemployed in the previous month. The problem states that the current unemployment decreased by $25\%$ from the previous month, so the equation is $x = 870 / (1 - 0.25)$ . Solving for $x$ , we get $x = 1,160$ residents unemployed in the previous month.

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Problem 4102

Find the x-values where a function equals 0, or its $y$ -intercepts.

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Problem 4103

Solve the quadratic equation $4w^2 + 4w + 1 = 121$ .

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Problem 4104

Solve the linear equation $-9x = 18$ for the unknown variable $x$ .

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Problem 4105

Find the missing value in $\square + 3.2 = 7.8$ using the equation $7.8 - 3.2 = \square$ .

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Problem 4106

Find the smallest integer $x$ such that $3x + 5 > 16$ .

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Problem 4107

Solve $4^{3x} = 8$ by graphing. Approximate solutions are $x \approx 0.9, 0.6, 0.5, 1.5$ .

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Problem 4108

Solve the linear equation $9x - 6x = 16 - 13$ to find the value of $x$ .

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Problem 4109

Solve $4^{x}=243$ and round the solution to the nearest 10-thousandth.

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Problem 4110

Solve for $x$ in the inequality $7x - 1 - 7x \leq -10$ , and determine the type of solution.

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Problem 4111

Solve for $u$ where $78=6u$ . Simplify to $u=\frac{78}{6}$ .

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Problem 4112

Determine if parabola $f(x) = -x^2 + 8x - 12$ opens upward or downward. Find vertex and $x$ -intercepts.

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Problem 4113

Rewrite the quadratic equation $2x^2 + 7x + 6 = 0$ by completing the square.

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Problem 4114

Find the equivalent expression for $4^{-3}$ .

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Problem 4115

Solve for $x$ in the equation $-4=\frac{7 x-(-1)}{-8}$ .

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Problem 4116

Evaluate $14.35x-3.62$ when $x=-3\frac{4}{5}$ . Write the answer as a decimal.

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Problem 4117

Simplify the inequality $2 > \frac{x}{6} + 7$ and express the solution set.

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Problem 4118

Find the number of students who visited the art and science museums given that for every 5 art museum visitors, 4 visit the science museum, and the total number of students is 27. Solve for $x$ in the equation $5x + 4x = 27$ .

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Problem 4119

Determine if $x y + x$ is even when $x$ is even or $y$ is odd.

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Problem 4120

Solve for $x$ in the equation $t = (m + d)x$ . Simplify the solution.

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Problem 4121

Factor the expression $w^{3} - 125$ , which is the difference of two perfect cubes.

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Problem 4122

Solve $12x^2 + 6x = -5$ using any method. Solve each inequality and write the answer as an interval.

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Problem 4123

Determine if the product $5.5 \cdot \sqrt{5}$ is rational, irrational, or if there is not enough information.

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Problem 4124

Calculate the value of the expression $2(z+2)-\frac{k}{8}$ when $z=5$ and $k=-24$ .

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Problem 4125

Determine the standard form equation of $9x^2 - 7x = 0$ and find the values of $a, b,$ and $c$ .

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Problem 4126

Find the degree, leading coefficients, and maximum real zeros of $f(x) = 2 x^{5} - 6 x^{3} - 2 x^{6} - 3$ .
Degree = 6 Leading Coefficient = -2 Maximum number of real zeros = 5

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Problem 4127

Find the cube root of 125 in radical and exponential notation.
$\sqrt[3]{125}$ , $125^{1/3}$

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Problem 4128

Write the sentence as an equation, where $p$ is the quotient of $a$ and 217.

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Problem 4129

Solve for $w$ in the equation $8w = 48$ .

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Problem 4130

Simplify absolute value expressions when the inner expressions are equal or opposites. $|5x-15|=|10x+17|$

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Problem 4131

Find a quadratic equation $y = ax^2 + bx + c$ that passes through the points $(0,12), (-6,0)$ , and $(2,0)$ .

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Problem 4132

Simplify the expression $(20-19i) + (11+8i)$ and $\sqrt{x}$ , write answers in standard form $(a+bi)$ .

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Problem 4133

Find values of $x$ and $p$ where $x$ is 8 less than some value, and $p$ is 6 more than 42.

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Problem 4134

Find the value of $9v+4$ given $-11v-7=4$ . Simplify the result $\prod$ .

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Problem 4135

Find the distance between the line $y=4+8x$ and the origin.

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Problem 4136

Solve for $x$ in the equation $3(5-x)=7x-2$ .

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Problem 4137

Translate the sentence "Vidya's savings decreased by 11 is 51" into an equation using the variable $v$ to represent Vidya's savings.

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Problem 4138

Solve the absolute value equation $2|x|=16$ . Explain your reasoning.

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Problem 4139

Find the value of $x$ where $\frac{1}{2} x - 5 = 8$ .

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Problem 4140

Solve the system of equations $3x + 2y = 2$ and $-3x + 5y = 5$ using the Addition Method to find the value of $x$ .

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Problem 4141

Find the cost of a desktop and laptop computer before finance charges, given the laptop costs $\$300$ less than the desktop, and the total finance charges for one year are $\$398$ at annual interest rates of $7\%$ and $6\%$ respectively. Desktop: $\$[1]$ Laptop: $\$[2]$

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Problem 4142

Factorize the following expressions using the binomial formula: (a) $a^{2}-25$ , (b) $b^{2}-100$ , (c) $9 a^{2}-25 b^{2}$ .

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Problem 4143

Solve the inequality $6|w| > 30$ . If all real numbers are solutions, click "All reals". If no solution, click "No solution".

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Problem 4144

Simplify the expression $2.5(m-2)+5.6 m$ .

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Problem 4145

Find the $x$ -intercept of the line $y = -\frac{1}{2}x + 2$ .

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Problem 4146

Solve $4|y| \leq 24$ . Find all real numbers $y$ that satisfy the inequality. If all reals are solutions, select "All reals". If no solution exists, select "No solution".

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Problem 4147

Find the $y$ -intercept of the function $h(x) = 18(2.5)^{x}$ .

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Problem 4148

Combine like terms to find the equivalent expression for each equation: $5x - 9 + 4x + 3 = \square$ , $8y + 2 - 6y + 3 = \square$ , $4x - 8 + 3x - 1 = \square$ , $-7y + 2 - y + 6 = \square$ .

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Problem 4149

Find the set of real numbers $d$ that satisfy the inequality $4d > -12$ .

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Problem 4150

Solve for $u$ in the equation $9 u - 30 = 5 u - 6$ . Simplify the solution for $u$ .

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Problem 4151

Find the price $x$ that maximizes the profit $y=-2x^2 + 135x - 844$ for a company selling widgets.

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Problem 4152

Solve the quadratic equation $2x^2 + 5x = 0$ to find one of its roots.

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Problem 4153

Simplify the expression $\frac{32 x y-20 y}{-4 y}$ .

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Problem 4154

Graph linear equations, find system solution. $y=\frac{1}{2}x+2, y=-x+5$

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Problem 4155

Simplify the expression $-3(8x) + 6(4x)$ when $x=2$ .

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Problem 4156

Find the set of real numbers x satisfying the inequality $x-2 \geq 10$ .

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Problem 4157

Find the rate of change between the points $(-13,-4)$ and $(7,6)$ . Record the answer as a decimal value.

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Problem 4158

Add the expressions $4m + 7$ and $-7m + 9$ .

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Problem 4159

Solve for $x$ in the equation $3(6+x)=78$ .

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Problem 4160

Solve for the result of subtracting the equations $-3x + 4y = 5$ from $8x - 4y = -4$ .

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Problem 4161

Solve for $y$ in the equation $9y + 7 = 10x - 3$ .

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Problem 4162

Solve for $z$ where $z+1=3.3$ .

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Problem 4163

Find the algebraic expression for "the quotient of $x$ and $6y$ ". Options: $\frac{x}{6}$ , $\frac{x}{6y}$ , $6xy$ , $x-6y$ .

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Problem 4164

Multiply $(x-3)(4x+2)$ using the distributive property. Select the correct distribution.

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Problem 4165

Find the value of $a$ in the equation $x^{2} x^{\frac{1}{5}}=x^{a}$ by evaluating the left-hand side in simplest form.

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Problem 4166

Determine the type of function represented by the equation $y=5$ : constant, identity, absolute value, or quadratic.

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Problem 4167

Solve for $t$ in the equation $18=3(2+t)$ .

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Problem 4168

Find the sum of $4d$ and $6d$ .

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Problem 4169

Solve the linear equation $\frac{x+2y}{7}=4$ for $x$ and $y$ .

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Problem 4170

Simplify the difference of two rational expressions: $(x^2 - x - 6)/(x + 2) - (x^2 - 6x + 5)/(x - 5)$ .

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Problem 4171

Solve for the value of $x$ given the equation $0.6x = 4.8$ . Enter the solution for $x$ in the box.

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Problem 4172

Find the value of the expression $8^{-\frac{1}{2}} \cdot 8^{\frac{7}{6}}$ .

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Problem 4173

Solve the equation $g[g(x)]=g(x)$ for $x$ , where $g(x)=3x+8$ .

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Problem 4174

Solve the inequality $5.8-0.9x \leq 19.3$ and check the solution.

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Problem 4175

Solve each equation by considering both sides and finding the variable value that makes them equal. Avoid standard algebraic techniques. Explain your reasoning. 1. $382+49=x+380$

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Problem 4176

Find the 16th square number using the formula $S_n = n^2$ . The 16th square number is $\square$ .

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Problem 4177

Find the value of $f(144)$ given that $f(x) = \frac{x}{72}$ .

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Problem 4178

Identify the equation that represents the transformation of a cubic function: $y=x+5$ , $y=(x+5)^{2}$ , $y=(x+5)^{3}$ , $y=|x+5|$ .

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Problem 4179

Find the value from $\{0, 1, 17, 72\}$ that satisfies the equation $n + 8 = 9$ .

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Problem 4180

Find the value of $f(-6.75)$ given $f(x) = \frac{x}{1.25}$ .

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Problem 4181

Select equations where $q$ is inversely proportional to $r$ , such as $q=\frac{4}{r}$ and $q=\frac{r}{4}$ .

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Problem 4182

Find the value of $8 + (w/4)$ when $w = 16$ .

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Problem 4183

Which variable in the equation $y=-5x+2$ is independent? A. $x$ B. $y$ C. both $x$ and $y$ D. neither $x$ nor $y$

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Problem 4184

Solve for $x$ in the equation $-28=3.5x$ .

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Problem 4185

Solve for $y$ in the equation $12.5=-1.3+\frac{y}{7}$ .

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Problem 4186

Find the remainder when dividing $2x^3 - x^2 + 4x - 5$ by $x - 3$ .

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Problem 4187

Expand the expression $(x^2 + 4)(x^2 - 6)$ and write the result as a polynomial in standard form.

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Problem 4188

Solve for the value of $v$ in the equation $-4=3+v$ .

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Problem 4189

Find the value of $b$ given the equation $(b-a)m=r$ .

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Problem 4190

Solve the linear equation $2y - 4 = 14$ and select the correct answer.

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Problem 4191

Solve the exponential equation $4^{x}=\frac{1}{\sqrt{2}}$ by expressing each side as a power and equating exponents.

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Problem 4192

Find the total points available on Mr. Frank's math tests, given that each test is worth 100 points, and there are 3 extra credit problems worth $x$ points each.

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Problem 4193

Solve expressions with given values $a=4, b=-8, c=6$ . Show work for $b+5, a-9, 4c, -3d, 18\div b, b^2, 5d+3, a+b, c-d, -2a-c$ .

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Problem 4194

Find the value of $b$ that makes $6.8x + b$ equivalent to $3.4(2x - 8)$ .

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Problem 4195

Find the possible values of $x$ when $x < -3$ .

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Problem 4196

Plot the inequality $-20>b$ on a number line.

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Problem 4197

Find the value of the geometric mean of 5 and 125. ( $\sqrt{5 \times 125} = 2\sqrt{30}$ )

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Problem 4198

Find the value of the constant $c$ in the equation $-4(2x^2 - 3) = -8x^2 + c$ .

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Problem 4199

Solve the inequality $2|v| > 14$ . If all real numbers are solutions, click "All reals". If no solution, click "No solution".

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Problem 4200

Identify the quadratic equation in standard form: $9=x^{2}$ , $0=5 x^{2}-6 x-1$ , $(x+5)(x-4)=0$ , $x^{2}-7 x=5$

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Algebra

Problem 4101

Problem 4102

Find the x-values where a function equals 0, or its yyy-intercepts.

Problem 4103

Solve the quadratic equation 4w2+4w+1=1214w^2 + 4w + 1 = 1214w2+4w+1=121.

Problem 4104

Solve the linear equation −9x=18-9x = 18−9x=18 for the unknown variable xxx.

Problem 4105

Find the missing value in □+3.2=7.8\square + 3.2 = 7.8□+3.2=7.8 using the equation 7.8−3.2=□7.8 - 3.2 = \square7.8−3.2=□.

Problem 4106

Find the smallest integer xxx such that 3x+5>163x + 5 > 163x+5>16.

Problem 4107

Solve 43x=84^{3x} = 843x=8 by graphing. Approximate solutions are x≈0.9,0.6,0.5,1.5x \approx 0.9, 0.6, 0.5, 1.5x≈0.9,0.6,0.5,1.5.

Problem 4108

Solve the linear equation 9x−6x=16−139x - 6x = 16 - 139x−6x=16−13 to find the value of xxx.

Problem 4109

Solve 4x=2434^{x}=2434x=243 and round the solution to the nearest 10-thousandth.

Problem 4110

Solve for xxx in the inequality 7x−1−7x≤−107x - 1 - 7x \leq -107x−1−7x≤−10, and determine the type of solution.

Problem 4111

Solve for uuu where 78=6u78=6u78=6u. Simplify to u=786u=\frac{78}{6}u=678​.

Problem 4112

Determine if parabola f(x)=−x2+8x−12f(x) = -x^2 + 8x - 12f(x)=−x2+8x−12 opens upward or downward. Find vertex and xxx-intercepts.

Problem 4113

Rewrite the quadratic equation 2x2+7x+6=02x^2 + 7x + 6 = 02x2+7x+6=0 by completing the square.

Problem 4114

Find the equivalent expression for 4−34^{-3}4−3.

Problem 4115

Solve for xxx in the equation −4=7x−(−1)−8-4=\frac{7 x-(-1)}{-8}−4=−87x−(−1)​.

Problem 4116

Evaluate 14.35x−3.6214.35x-3.6214.35x−3.62 when x=−345x=-3\frac{4}{5}x=−354​. Write the answer as a decimal.

Problem 4117

Simplify the inequality 2>x6+72 > \frac{x}{6} + 72>6x​+7 and express the solution set.

Problem 4118

Find the number of students who visited the art and science museums given that for every 5 art museum visitors, 4 visit the science museum, and the total number of students is 27. Solve for xxx in the equation 5x+4x=275x + 4x = 275x+4x=27.

Problem 4119

Determine if xy+xx y + xxy+x is even when xxx is even or yyy is odd.

Problem 4120

Solve for xxx in the equation t=(m+d)xt = (m + d)xt=(m+d)x. Simplify the solution.

Problem 4121

Factor the expression w3−125w^{3} - 125w3−125, which is the difference of two perfect cubes.

Problem 4122

Solve 12x2+6x=−512x^2 + 6x = -512x2+6x=−5 using any method. Solve each inequality and write the answer as an interval.

Problem 4123

Determine if the product 5.5⋅55.5 \cdot \sqrt{5}5.5⋅5​ is rational, irrational, or if there is not enough information.

Problem 4124

Calculate the value of the expression 2(z+2)−k82(z+2)-\frac{k}{8}2(z+2)−8k​ when z=5z=5z=5 and k=−24k=-24k=−24.

Problem 4125

Determine the standard form equation of 9x2−7x=09x^2 - 7x = 09x2−7x=0 and find the values of a,b,a, b,a,b, and ccc.

Problem 4126

Find the degree, leading coefficients, and maximum real zeros of f(x)=2x5−6x3−2x6−3f(x) = 2 x^{5} - 6 x^{3} - 2 x^{6} - 3f(x)=2x5−6x3−2x6−3.Degree = 6 Leading Coefficient = -2 Maximum number of real zeros = 5

Problem 4127

Find the cube root of 125 in radical and exponential notation.1253\sqrt[3]{125}3125​, 1251/3125^{1/3}1251/3

Problem 4128

Write the sentence as an equation, where ppp is the quotient of aaa and 217.

Problem 4129

Solve for www in the equation 8w=488w = 488w=48.

Problem 4130

Simplify absolute value expressions when the inner expressions are equal or opposites. ∣5x−15∣=∣10x+17∣|5x-15|=|10x+17|∣5x−15∣=∣10x+17∣

Problem 4131

Find a quadratic equation y=ax2+bx+cy = ax^2 + bx + cy=ax2+bx+c that passes through the points (0,12),(−6,0)(0,12), (-6,0)(0,12),(−6,0), and (2,0)(2,0)(2,0).

Problem 4132

Simplify the expression (20−19i)+(11+8i)(20-19i) + (11+8i)(20−19i)+(11+8i) and x\sqrt{x}x​, write answers in standard form (a+bi)(a+bi)(a+bi).

Problem 4133

Find values of xxx and ppp where xxx is 8 less than some value, and ppp is 6 more than 42.

Problem 4134

Find the value of 9v+49v+49v+4 given −11v−7=4-11v-7=4−11v−7=4. Simplify the result ∏\prod∏.

Problem 4135

Find the distance between the line y=4+8xy=4+8xy=4+8x and the origin.

Problem 4136

Solve for xxx in the equation 3(5−x)=7x−23(5-x)=7x-23(5−x)=7x−2.

Problem 4137

Translate the sentence "Vidya's savings decreased by 11 is 51" into an equation using the variable vvv to represent Vidya's savings.

Problem 4138

Solve the absolute value equation 2∣x∣=162|x|=162∣x∣=16. Explain your reasoning.

Problem 4139

Find the value of xxx where 12x−5=8\frac{1}{2} x - 5 = 821​x−5=8.

Problem 4140

Solve the system of equations 3x+2y=23x + 2y = 23x+2y=2 and −3x+5y=5-3x + 5y = 5−3x+5y=5 using the Addition Method to find the value of xxx.

Find the x-values where a function equals 0, or its $y$ -intercepts.

Solve the quadratic equation $4w^2 + 4w + 1 = 121$ .

Solve the linear equation $-9x = 18$ for the unknown variable $x$ .

Find the missing value in $\square + 3.2 = 7.8$ using the equation $7.8 - 3.2 = \square$ .

Find the smallest integer $x$ such that $3x + 5 > 16$ .

Solve $4^{3x} = 8$ by graphing. Approximate solutions are $x \approx 0.9, 0.6, 0.5, 1.5$ .

Solve the linear equation $9x - 6x = 16 - 13$ to find the value of $x$ .

Solve $4^{x}=243$ and round the solution to the nearest 10-thousandth.

Solve for $x$ in the inequality $7x - 1 - 7x \leq -10$ , and determine the type of solution.

Solve for $u$ where $78=6u$ . Simplify to $u=\frac{78}{6}$ .

Determine if parabola $f(x) = -x^2 + 8x - 12$ opens upward or downward. Find vertex and $x$ -intercepts.

Rewrite the quadratic equation $2x^2 + 7x + 6 = 0$ by completing the square.

Find the equivalent expression for $4^{-3}$ .

Solve for $x$ in the equation $-4=\frac{7 x-(-1)}{-8}$ .

Evaluate $14.35x-3.62$ when $x=-3\frac{4}{5}$ . Write the answer as a decimal.

Simplify the inequality $2 > \frac{x}{6} + 7$ and express the solution set.

Find the number of students who visited the art and science museums given that for every 5 art museum visitors, 4 visit the science museum, and the total number of students is 27. Solve for $x$ in the equation $5x + 4x = 27$ .

Determine if $x y + x$ is even when $x$ is even or $y$ is odd.

Solve for $x$ in the equation $t = (m + d)x$ . Simplify the solution.

Factor the expression $w^{3} - 125$ , which is the difference of two perfect cubes.

Solve $12x^2 + 6x = -5$ using any method. Solve each inequality and write the answer as an interval.

Determine if the product $5.5 \cdot \sqrt{5}$ is rational, irrational, or if there is not enough information.

Calculate the value of the expression $2(z+2)-\frac{k}{8}$ when $z=5$ and $k=-24$ .

Determine the standard form equation of $9x^2 - 7x = 0$ and find the values of $a, b,$ and $c$ .

Find the degree, leading coefficients, and maximum real zeros of $f(x) = 2 x^{5} - 6 x^{3} - 2 x^{6} - 3$ .
Degree = 6 Leading Coefficient = -2 Maximum number of real zeros = 5

Find the cube root of 125 in radical and exponential notation.
$\sqrt[3]{125}$ , $125^{1/3}$

Write the sentence as an equation, where $p$ is the quotient of $a$ and 217.

Solve for $w$ in the equation $8w = 48$ .

Simplify absolute value expressions when the inner expressions are equal or opposites. $|5x-15|=|10x+17|$

Find a quadratic equation $y = ax^2 + bx + c$ that passes through the points $(0,12), (-6,0)$ , and $(2,0)$ .

Simplify the expression $(20-19i) + (11+8i)$ and $\sqrt{x}$ , write answers in standard form $(a+bi)$ .

Find values of $x$ and $p$ where $x$ is 8 less than some value, and $p$ is 6 more than 42.

Find the value of $9v+4$ given $-11v-7=4$ . Simplify the result $\prod$ .

Find the distance between the line $y=4+8x$ and the origin.

Solve for $x$ in the equation $3(5-x)=7x-2$ .

Translate the sentence "Vidya's savings decreased by 11 is 51" into an equation using the variable $v$ to represent Vidya's savings.

Solve the absolute value equation $2|x|=16$ . Explain your reasoning.

Find the value of $x$ where $\frac{1}{2} x - 5 = 8$ .

Solve the system of equations $3x + 2y = 2$ and $-3x + 5y = 5$ using the Addition Method to find the value of $x$ .

Find the cost of a desktop and laptop computer before finance charges, given the laptop costs $\$300$ less than the desktop, and the total finance charges for one year are $\$398$ at annual interest rates of $7\%$ and $6\%$ respectively. Desktop: $\$[1]$ Laptop: $\$[2]$

Factorize the following expressions using the binomial formula: (a) $a^{2}-25$ , (b) $b^{2}-100$ , (c) $9 a^{2}-25 b^{2}$ .

Solve the inequality $6|w| > 30$ . If all real numbers are solutions, click "All reals". If no solution, click "No solution".

Simplify the expression $2.5(m-2)+5.6 m$ .

Find the $x$ -intercept of the line $y = -\frac{1}{2}x + 2$ .

Solve $4|y| \leq 24$ . Find all real numbers $y$ that satisfy the inequality. If all reals are solutions, select "All reals". If no solution exists, select "No solution".

Find the $y$ -intercept of the function $h(x) = 18(2.5)^{x}$ .

Find the set of real numbers $d$ that satisfy the inequality $4d > -12$ .

Solve for $u$ in the equation $9 u - 30 = 5 u - 6$ . Simplify the solution for $u$ .

Find the price $x$ that maximizes the profit $y=-2x^2 + 135x - 844$ for a company selling widgets.

Solve the quadratic equation $2x^2 + 5x = 0$ to find one of its roots.

Simplify the expression $\frac{32 x y-20 y}{-4 y}$ .

Graph linear equations, find system solution. $y=\frac{1}{2}x+2, y=-x+5$

Simplify the expression $-3(8x) + 6(4x)$ when $x=2$ .

Find the set of real numbers x satisfying the inequality $x-2 \geq 10$ .

Find the rate of change between the points $(-13,-4)$ and $(7,6)$ . Record the answer as a decimal value.

Add the expressions $4m + 7$ and $-7m + 9$ .

Solve for $x$ in the equation $3(6+x)=78$ .

Solve for the result of subtracting the equations $-3x + 4y = 5$ from $8x - 4y = -4$ .

Solve for $y$ in the equation $9y + 7 = 10x - 3$ .

Solve for $z$ where $z+1=3.3$ .

Find the algebraic expression for "the quotient of $x$ and $6y$ ". Options: $\frac{x}{6}$ , $\frac{x}{6y}$ , $6xy$ , $x-6y$ .

Multiply $(x-3)(4x+2)$ using the distributive property. Select the correct distribution.

Find the value of $a$ in the equation $x^{2} x^{\frac{1}{5}}=x^{a}$ by evaluating the left-hand side in simplest form.

Determine the type of function represented by the equation $y=5$ : constant, identity, absolute value, or quadratic.

Solve for $t$ in the equation $18=3(2+t)$ .

Find the sum of $4d$ and $6d$ .

Solve the linear equation $\frac{x+2y}{7}=4$ for $x$ and $y$ .

Simplify the difference of two rational expressions: $(x^2 - x - 6)/(x + 2) - (x^2 - 6x + 5)/(x - 5)$ .

Solve for the value of $x$ given the equation $0.6x = 4.8$ . Enter the solution for $x$ in the box.

Find the value of the expression $8^{-\frac{1}{2}} \cdot 8^{\frac{7}{6}}$ .

Solve the equation $g[g(x)]=g(x)$ for $x$ , where $g(x)=3x+8$ .

Solve the inequality $5.8-0.9x \leq 19.3$ and check the solution.