Browse Math problems in the Studdy Learning Bank!

Problem 4101

Solve the absolute value equation $|\\frac{7x - 5}{7 - x}| = 8$ for $x$ .

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Problem 4102

Solve the linear equation $2 \cdot x + 5 = 10$ for the value of $x$ .

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Problem 4103

Finden Sie den Schnittpunkt der Funktionen $f(x) = -0.5x + 2$ und $g(x) = x - 1$ .

See Solution

Problem 4104

Simplify the expression $(13x+21)-(5x-9)$ into an equivalent binomial, then test the equivalence using a calculator and provide evidence.

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Problem 4105

Solve for $x$ in the linear equation $y=4x+8$ .

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Problem 4106

Analyze the symmetry of the function $f(x) = x \cdot e^{x}$ .

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Problem 4107

Solve the quadratic equation $x^2 + 7x = 3$ and find the two real solutions.

See Solution

Problem 4108

Berechne Mittelwert, Median und Quartilsabstand für die Datenreihe: $3 ; 8 ; 12 ; 5 ; 7 ; 8 ; 9,5 ; 11 ; 14 ; 6 ; 8,5$ .

See Solution

Problem 4109

Berechnen Sie die Ableitung der Funktion $f(x) = \sin(6x)$ .

See Solution

Problem 4110

Find the value of $x$ when $9(3^{x})=27^{3}$ .

See Solution

Problem 4111

Solve for x in the equation $3x + 4 = 2x - 5$ by subtracting 5 from both sides and then subtracting $2x$ from both sides.

See Solution

Problem 4112

Solve the equation $5x - 2 = 4 + 2x$ for $x$ and enter the number in the green box.

See Solution

Problem 4113

Find the expression for the difference between 3 and 5 times a number.

See Solution

Problem 4114

Evaluate the formula $E=z \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$ for given values of $z$ , $\hat{p}$ , and $n$ . Round the result to three decimal places.

See Solution

Problem 4115

Find the values of $x$ and $y$ that satisfy the linear equation $30x + 50y = 2400$ .

See Solution

Problem 4116

Find the general form of the equation $x=\frac{1}{3} y$ .

See Solution

Problem 4117

Evaluate the expression $3.99 \times 10^{2}$ .

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Problem 4118

Solve the linear equation $2x + 75 = 102 - x$ and prove that $z = 9$ .

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Problem 4119

Find the percentage of people with IQ scores between $88$ and $116$ in a normal distribution with $\mu=100$ and $\sigma=15$ , rounded to the nearest tenth.

See Solution

Problem 4120

Find the number of boxes of candy if each box contains an unknown number of candies and the total number of candies is 3.

See Solution

Problem 4121

Solve the linear equation $6.81 - \frac{4x}{7} = 21$ for the unknown variable $x$ .

See Solution

Problem 4122

Solve for $b$ in the equation $-1=-0.5 \cdot 14 + b$ .

See Solution

Problem 4123

Find the number of real zeros, end behavior, and max turns of the cubic function $f(x) = -x^3$ .

See Solution

Problem 4124

Find the values of $x$ that satisfy the inequality $|x| \leq 3.5$ .

See Solution

Problem 4125

Finden Sie die Nullstellen der Kubikfunktion $f(x)=3x^3+3x^2-18x$ durch Ausklammern.

See Solution

Problem 4126

Find the absolute value of $\frac{3}{4}$ .

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Problem 4127

A patient lost $5$ pounds per month for $15$ months. What is their net change in weight?

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Problem 4128

Berechne die Potenzen: $2^{4}, (-2)^{3}, 4^{4}, (1/3)^{2}, (2/3)^{3}, (1/5)^{4}, 5^{-2}, 4^{-3}, (-3)^{-4}, (-2)^{-3}, (2 \cdot 3)^{-3}, 0^{5}$

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Problem 4129

Calculate the total cost $K(x)$ when the production quantity $x$ is 4000 units and the variable cost per unit is €3.20, and the fixed cost is €6400.

See Solution

Problem 4130

Calculate the cube of $5.00 \times 10^{11}$ and express the result in scientific notation.

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Problem 4131

Find the value of $x$ that satisfies the equation $21=3x$ .

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Problem 4132

Solve the inequality $13.5-x \neq 6$ for real values of $x$ .

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Problem 4133

Use the difference of two squares to find the following products: $34 \cdot 26$ , $22 \cdot 28$ , $17 \cdot 7$ .

See Solution

Problem 4134

Find the sum of the first 10 consecutive odd numbers starting from 13.

See Solution

Problem 4135

Solve the linear equation $2n + 11 + 4n + 3 = 8n$ to find the value of $n$ .

See Solution

Problem 4136

Calculate the square of the sum of -58.8 and 49.4.

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Problem 4137

Find the quadratic function with points $(0,5), (2,11), (-1,14)$ . The equation is $y=ax^2+bx+c$ .

See Solution

Problem 4138

Finde die Nullstellen der quadratischen Funktion $f(x)=x^{2}-10x+25$ .

See Solution

Problem 4139

Find power function $y=a \times b^x$ and linear function $y=mx+c$ to model data set $(x, y)$ . Power function coefficients $a=4.287$ , $b=1.204$ . Determine which function better fits the data.

See Solution

Problem 4140

Find the standard form equation for $y=3x-\frac{1}{5}$ .

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Problem 4141

Determine if the equation $5+3=2\left(\frac{5+7}{3}\right)$ is true, false, or an open equation.

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Problem 4142

Solve for x in the linear equation $-10+x=18$ .

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Problem 4143

Solve the equation $2+3(2x-4)=3(4x-2)$ . Which statement is true? $x=0$ is a solution, or $x=-\frac{2}{3}$ is a solution.

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Problem 4144

How long will the 12-inch candle last with a burning rate of 1 inch per hour when the power is out for 5 hours?

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Problem 4145

Finde die Funktionsgleichung einer linearen Funktion mit Steigung $m=-2$ , die durch den Punkt $\mathbf{P (-7/-5)}$ verläuft.

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Problem 4146

Solve the proportion $\frac{-9}{7}=\frac{p}{63}$ and check. The solution set is { $p$ }.

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Problem 4147

A fruit bowl has bananas, lemons, and apples. The ratio of bananas to lemons is $4:5$ . The probability of picking a banana is $\frac{1}{3}$ . Find the probability of picking an apple.

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Problem 4148

Solve for $x$ given $m \angle 2 = x + 42$ and $m \angle 2 = 72$ .

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Problem 4149

Find the number that completes the perfect square for $x^2 + 8x + \Box$ .

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Problem 4150

Solve $\frac{y}{2}-\frac{3}{2}x=-\frac{7}{2}$ for y or x, or rearrange to slope-intercept or standard form.

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Problem 4151

Determine which inequality statement is true: $1.2 < -6.9$ , $6.9 < 1.2$ , $-1.2 > 6.9$ , or $-6.9 < -1.2$ .

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Problem 4152

Solve for $p$ in the equation $11.9p + 23.1 = 273$ .

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Problem 4153

Solve the inequality $w - 3.5 \leq -2$ for the real number $w$ .

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Problem 4154

Simplify the expression $\frac{7 x^{2}+3 y^{2}}{2}$ with $x=4$ and $y=2$ .

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Problem 4155

Describe the graph of an odd function. Is it symmetric about $y=x$ , $x$ -axis, $x=0$ , or the origin?

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Problem 4156

Find the coefficient of the variable $y$ in the equation $-30y + 4 = 64$ .

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Problem 4157

Add $t$ and the sum of 8 and $u$ .

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Problem 4158

Find the coordinates of point $T$ if the midpoint of line $RT$ is $(3,0)$ and the coordinates of $R$ are $(-1,-4)$ .

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Problem 4159

Choose all true statements about the imaginary unit $i$ : $i^{2}=-1$ , $i=\sqrt{-1}$ , the solution of $x^{2}=-1$ .

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Problem 4160

Add, subtract, or compare two fractions: A marine biologist measured a fish $84/6$ feet long and another $11/2$ feet long. How much longer was the first fish? Express your answer as a fraction or whole/mixed number.

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Problem 4161

Solve the linear equation $-2x - y = 7$ for $y$ in terms of $x$ .

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Problem 4162

Determine the horizontal and vertical asymptotes of the function $\frac{e^{x}}{2 x}$ .

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Problem 4163

Identify the error in solving the equation $x - \frac{m}{3} = -4$ and provide the correct solution.

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Problem 4164

Find the value of $y$ for the quadratic function $y = -x^2 + 6x - 5$ when $x = 0.5$ .

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Problem 4165

Solve the linear equation $x=-x+2$ for the value of $x$ .

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Problem 4166

Publish a book: $25x + 1100 = y$ . Find the startup cost and cost change per book.

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Problem 4167

Subtract $\frac{1}{2}(x-4)(x-2)$ from $5x+10$ and simplify to $6+8x-\frac{1}{2}x^2$ .

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Problem 4168

Find the difference between the perimeters $P_1$ and $P_2$ of two figures, where the difference is $n$ . Write and solve an absolute value inequality to represent the situation.

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Problem 4169

Find the value of $x$ given the equation $3x + 2 = 8$ .

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Problem 4170

Find the value of $g$ that satisfies the inequality $9 + 5g > -1$ .

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Problem 4171

Find the property described by the statement: "If $a=b$ , then either $a$ or $b$ may be the other in any equation."

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Problem 4172

Solve the absolute value equation $|7x-5| = 39$ by finding two possible values for $7x-5$ .

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Problem 4173

Solve the system of linear inequalities: $5x < -20$ and $3x > 12$ .

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Problem 4174

Describe the transformation of the linear function $f(x) = \frac{1}{3}x$ .

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Problem 4175

Solve the absolute value inequality $|x-6|-4<4$ . First isolate the absolute value expression, then write the two inequalities to solve.

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Problem 4176

A construction crew built $2 \frac{1}{4}$ km of road per day for 14 days. Find the total length of road built.

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Problem 4177

Solve for $d$ in the equation $-3.8=d \div 1.5$ .

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Problem 4178

Solve the equation $\frac{x}{5}+11.3=-1.2$ for $x=T$ . Find the value of $T$ .

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Problem 4179

Evaluate the expression $7x^2 + 9x - 3$ when $x=3$ .

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Problem 4180

Determine if the solution to the equation $B=0.181818181818\dots$ is a rational or irrational number.

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Problem 4181

Identify values in the interval $-2 \leq x \leq 6$ from the given set: $x=0, -1, -4, 3, 6, -\frac{5}{4}$ .

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Problem 4182

Find the error in the plant's growth rate of $0.2 \text{cm/0.5 day}$ if it grows $3.6 \text{cm}$ in $1.44 \text{days}$ .

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Problem 4183

Solve for $x$ in the inequality $4(x+1) \leq 4x+3$ . The solution set is $x \leq 1$ or $x \leq 7$ .

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Problem 4184

Determine the end behavior of the graph of the function $f(x) = -3 x^{4} - 6 x^{2} + 9 x + 2$ .

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Problem 4185

Match the expressions in Column A with their respective equivalents in Column B.
Column A: $-(27+b)$ , $-(27-b)$ , $-(-27+b)$ , $-(-27-b)$ Column B: $-27-b$ , $27-b$ , $-27+b$ , $27+b$

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Problem 4186

Simplify the expression $7: 1245 \cdot 100$ .

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Problem 4187

Simplify the expression $7(x+3)$ by distribution. Fill in the blanks with the simplified expression.

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Problem 4188

Find the polar form solution for the equation $z^{4} + 16p^{2}i = 0$ , where $p$ is a real number.

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Problem 4189

Prove that the equation $-3y^6 + 8y^4 - 9y^2 + 10 = 0$ has exactly two real solutions. Find the discriminant of $-3x^2 + 2x - 5$ . (2 marks)

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Problem 4190

Find the pattern in the cost sequence: $4.50,$ 6.75, $9.00, ...

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Problem 4191

Find the values of $x$ where $f(x) = -x(x+4)^{2}(x+1)(x-6)^{6} \leq 0$ .

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Problem 4192

Find the volume $x$ in mL given the conversion rate $1 \mathrm{~mL}=2200$ units and a total of 5000 units.

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Problem 4193

Replace the missing operator in the expression $-6 ? 9$ with either $<$ or $>$ .

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Problem 4194

Find the sum of the numbers $703.23$ , $77.8$ , $6$ , $25.6$ , and $18.9$ .

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Problem 4195

Find $m$ and determine the $x$ , $y$ intercepts of $f(x)=x^{3}-5x^{2}+mx+9$ , where $(x+1)$ is a factor. Find the stationary points and concavity, then sketch $f(x)$ .

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Problem 4196

Solve for the unknown variable $Z$ given the equation $X=\frac{2}{9}(Y+Z)$ .

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Problem 4197

Divide $\frac{2}{7}$ by $-5$ and find the result.

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Problem 4198

Find the general form of a quadratic function $f(x) = (x + 7)^2$ .

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Problem 4199

Expand the expression $f(x) = (2 - x)^2$ .

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Problem 4200

Calculate the initial payment for a safari holiday for 4 people. The holiday costs $£ 2000$ per person and the admin fee is $£ 25$ . The formula is $p=a+\frac{n c}{10}$ , where $p$ is the initial payment (£) and $a$ is the admin fee (£).

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Math

Problem 4101

Solve the absolute value equation ∣frac7x−57−x∣=8|\\frac{7x - 5}{7 - x}| = 8∣frac7x−57−x∣=8 for xxx.

Problem 4102

Solve the linear equation 2⋅x+5=102 \cdot x + 5 = 102⋅x+5=10 for the value of xxx.

Problem 4103

Finden Sie den Schnittpunkt der Funktionen f(x)=−0.5x+2f(x) = -0.5x + 2f(x)=−0.5x+2 und g(x)=x−1g(x) = x - 1g(x)=x−1.

Problem 4104

Simplify the expression (13x+21)−(5x−9)(13x+21)-(5x-9)(13x+21)−(5x−9) into an equivalent binomial, then test the equivalence using a calculator and provide evidence.

Problem 4105

Solve for xxx in the linear equation y=4x+8y=4x+8y=4x+8.

Problem 4106

Analyze the symmetry of the function f(x)=x⋅exf(x) = x \cdot e^{x}f(x)=x⋅ex.

Problem 4107

Solve the quadratic equation x2+7x=3x^2 + 7x = 3x2+7x=3 and find the two real solutions.

Problem 4108

Berechne Mittelwert, Median und Quartilsabstand für die Datenreihe: 3;8;12;5;7;8;9,5;11;14;6;8,53 ; 8 ; 12 ; 5 ; 7 ; 8 ; 9,5 ; 11 ; 14 ; 6 ; 8,53;8;12;5;7;8;9,5;11;14;6;8,5.

Problem 4109

Berechnen Sie die Ableitung der Funktion f(x)=sin⁡(6x)f(x) = \sin(6x)f(x)=sin(6x).

Problem 4110

Find the value of xxx when 9(3x)=2739(3^{x})=27^{3}9(3x)=273.

Problem 4111

Solve for x in the equation 3x+4=2x−53x + 4 = 2x - 53x+4=2x−5 by subtracting 5 from both sides and then subtracting 2x2x2x from both sides.

Problem 4112

Solve the equation 5x−2=4+2x5x - 2 = 4 + 2x5x−2=4+2x for xxx and enter the number in the green box.

Problem 4113

Find the expression for the difference between 3 and 5 times a number.

Problem 4114

Evaluate the formula E=zp^(1−p^)nE=z \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}E=znp^​(1−p^​)​​ for given values of zzz, p^\hat{p}p^​, and nnn. Round the result to three decimal places.

Problem 4115

Find the values of xxx and yyy that satisfy the linear equation 30x+50y=240030x + 50y = 240030x+50y=2400.

Problem 4116

Find the general form of the equation x=13yx=\frac{1}{3} yx=31​y.

Problem 4117

Evaluate the expression 3.99×1023.99 \times 10^{2}3.99×102.

Problem 4118

Solve the linear equation 2x+75=102−x2x + 75 = 102 - x2x+75=102−x and prove that z=9z = 9z=9.

Problem 4119

Find the percentage of people with IQ scores between 888888 and 116116116 in a normal distribution with μ=100\mu=100μ=100 and σ=15\sigma=15σ=15, rounded to the nearest tenth.

Problem 4120

Find the number of boxes of candy if each box contains an unknown number of candies and the total number of candies is 3.

Problem 4121

Solve the linear equation 6.81−4x7=216.81 - \frac{4x}{7} = 216.81−74x​=21 for the unknown variable xxx.

Problem 4122

Solve for bbb in the equation −1=−0.5⋅14+b-1=-0.5 \cdot 14 + b−1=−0.5⋅14+b.

Problem 4123

Find the number of real zeros, end behavior, and max turns of the cubic function f(x)=−x3f(x) = -x^3f(x)=−x3.

Problem 4124

Find the values of xxx that satisfy the inequality ∣x∣≤3.5|x| \leq 3.5∣x∣≤3.5.

Problem 4125

Finden Sie die Nullstellen der Kubikfunktion f(x)=3x3+3x2−18xf(x)=3x^3+3x^2-18xf(x)=3x3+3x2−18x durch Ausklammern.

Problem 4126

Find the absolute value of 34\frac{3}{4}43​.

Problem 4127

A patient lost 555 pounds per month for 151515 months. What is their net change in weight?

Problem 4128

Problem 4129

Calculate the total cost K(x)K(x)K(x) when the production quantity xxx is 4000 units and the variable cost per unit is €3.20, and the fixed cost is €6400.

Problem 4130

Calculate the cube of 5.00×10115.00 \times 10^{11}5.00×1011 and express the result in scientific notation.

Problem 4131

Find the value of xxx that satisfies the equation 21=3x21=3x21=3x.

Problem 4132

Solve the inequality 13.5−x≠613.5-x \neq 613.5−x=6 for real values of xxx.

Problem 4133

Use the difference of two squares to find the following products: 34⋅2634 \cdot 2634⋅26, 22⋅2822 \cdot 2822⋅28, 17⋅717 \cdot 717⋅7.

Problem 4134

Find the sum of the first 10 consecutive odd numbers starting from 13.

Problem 4135

Solve the linear equation 2n+11+4n+3=8n2n + 11 + 4n + 3 = 8n2n+11+4n+3=8n to find the value of nnn.

Problem 4136

Calculate the square of the sum of -58.8 and 49.4.

Problem 4137

Find the quadratic function with points (0,5),(2,11),(−1,14)(0,5), (2,11), (-1,14)(0,5),(2,11),(−1,14). The equation is y=ax2+bx+cy=ax^2+bx+cy=ax2+bx+c.

Problem 4138

Finde die Nullstellen der quadratischen Funktion f(x)=x2−10x+25f(x)=x^{2}-10x+25f(x)=x2−10x+25.

Problem 4139

Find power function y=a×bxy=a \times b^xy=a×bx and linear function y=mx+cy=mx+cy=mx+c to model data set (x,y)(x, y)(x,y). Power function coefficients a=4.287a=4.287a=4.287, b=1.204b=1.204b=1.204. Determine which function better fits the data.

Problem 4140

Find the standard form equation for y=3x−15y=3x-\frac{1}{5}y=3x−51​.

Solve the absolute value equation $|\\frac{7x - 5}{7 - x}| = 8$ for $x$ .

Solve the linear equation $2 \cdot x + 5 = 10$ for the value of $x$ .

Finden Sie den Schnittpunkt der Funktionen $f(x) = -0.5x + 2$ und $g(x) = x - 1$ .

Simplify the expression $(13x+21)-(5x-9)$ into an equivalent binomial, then test the equivalence using a calculator and provide evidence.

Solve for $x$ in the linear equation $y=4x+8$ .

Analyze the symmetry of the function $f(x) = x \cdot e^{x}$ .

Solve the quadratic equation $x^2 + 7x = 3$ and find the two real solutions.

Berechne Mittelwert, Median und Quartilsabstand für die Datenreihe: $3 ; 8 ; 12 ; 5 ; 7 ; 8 ; 9,5 ; 11 ; 14 ; 6 ; 8,5$ .

Berechnen Sie die Ableitung der Funktion $f(x) = \sin(6x)$ .

Find the value of $x$ when $9(3^{x})=27^{3}$ .

Solve for x in the equation $3x + 4 = 2x - 5$ by subtracting 5 from both sides and then subtracting $2x$ from both sides.

Solve the equation $5x - 2 = 4 + 2x$ for $x$ and enter the number in the green box.

Evaluate the formula $E=z \sqrt{\frac{\hat{p}(1-\hat{p})}{n}}$ for given values of $z$ , $\hat{p}$ , and $n$ . Round the result to three decimal places.

Find the values of $x$ and $y$ that satisfy the linear equation $30x + 50y = 2400$ .

Find the general form of the equation $x=\frac{1}{3} y$ .

Evaluate the expression $3.99 \times 10^{2}$ .

Solve the linear equation $2x + 75 = 102 - x$ and prove that $z = 9$ .

Find the percentage of people with IQ scores between $88$ and $116$ in a normal distribution with $\mu=100$ and $\sigma=15$ , rounded to the nearest tenth.

Solve the linear equation $6.81 - \frac{4x}{7} = 21$ for the unknown variable $x$ .

Solve for $b$ in the equation $-1=-0.5 \cdot 14 + b$ .

Find the number of real zeros, end behavior, and max turns of the cubic function $f(x) = -x^3$ .

Find the values of $x$ that satisfy the inequality $|x| \leq 3.5$ .

Finden Sie die Nullstellen der Kubikfunktion $f(x)=3x^3+3x^2-18x$ durch Ausklammern.

Find the absolute value of $\frac{3}{4}$ .

A patient lost $5$ pounds per month for $15$ months. What is their net change in weight?

Calculate the total cost $K(x)$ when the production quantity $x$ is 4000 units and the variable cost per unit is €3.20, and the fixed cost is €6400.

Calculate the cube of $5.00 \times 10^{11}$ and express the result in scientific notation.

Find the value of $x$ that satisfies the equation $21=3x$ .

Solve the inequality $13.5-x \neq 6$ for real values of $x$ .

Use the difference of two squares to find the following products: $34 \cdot 26$ , $22 \cdot 28$ , $17 \cdot 7$ .

Solve the linear equation $2n + 11 + 4n + 3 = 8n$ to find the value of $n$ .

Find the quadratic function with points $(0,5), (2,11), (-1,14)$ . The equation is $y=ax^2+bx+c$ .

Finde die Nullstellen der quadratischen Funktion $f(x)=x^{2}-10x+25$ .

Find power function $y=a \times b^x$ and linear function $y=mx+c$ to model data set $(x, y)$ . Power function coefficients $a=4.287$ , $b=1.204$ . Determine which function better fits the data.

Find the standard form equation for $y=3x-\frac{1}{5}$ .

Determine if the equation $5+3=2\left(\frac{5+7}{3}\right)$ is true, false, or an open equation.

Solve for x in the linear equation $-10+x=18$ .

Solve the equation $2+3(2x-4)=3(4x-2)$ . Which statement is true? $x=0$ is a solution, or $x=-\frac{2}{3}$ is a solution.

Finde die Funktionsgleichung einer linearen Funktion mit Steigung $m=-2$ , die durch den Punkt $\mathbf{P (-7/-5)}$ verläuft.

Solve the proportion $\frac{-9}{7}=\frac{p}{63}$ and check. The solution set is { $p$ }.

A fruit bowl has bananas, lemons, and apples. The ratio of bananas to lemons is $4:5$ . The probability of picking a banana is $\frac{1}{3}$ . Find the probability of picking an apple.

Solve for $x$ given $m \angle 2 = x + 42$ and $m \angle 2 = 72$ .

Find the number that completes the perfect square for $x^2 + 8x + \Box$ .

Solve $\frac{y}{2}-\frac{3}{2}x=-\frac{7}{2}$ for y or x, or rearrange to slope-intercept or standard form.

Determine which inequality statement is true: $1.2 < -6.9$ , $6.9 < 1.2$ , $-1.2 > 6.9$ , or $-6.9 < -1.2$ .

Solve for $p$ in the equation $11.9p + 23.1 = 273$ .

Solve the inequality $w - 3.5 \leq -2$ for the real number $w$ .

Simplify the expression $\frac{7 x^{2}+3 y^{2}}{2}$ with $x=4$ and $y=2$ .

Describe the graph of an odd function. Is it symmetric about $y=x$ , $x$ -axis, $x=0$ , or the origin?

Find the coefficient of the variable $y$ in the equation $-30y + 4 = 64$ .

Add $t$ and the sum of 8 and $u$ .

Find the coordinates of point $T$ if the midpoint of line $RT$ is $(3,0)$ and the coordinates of $R$ are $(-1,-4)$ .

Choose all true statements about the imaginary unit $i$ : $i^{2}=-1$ , $i=\sqrt{-1}$ , the solution of $x^{2}=-1$ .

Add, subtract, or compare two fractions: A marine biologist measured a fish $84/6$ feet long and another $11/2$ feet long. How much longer was the first fish? Express your answer as a fraction or whole/mixed number.

Solve the linear equation $-2x - y = 7$ for $y$ in terms of $x$ .

Determine the horizontal and vertical asymptotes of the function $\frac{e^{x}}{2 x}$ .

Identify the error in solving the equation $x - \frac{m}{3} = -4$ and provide the correct solution.

Find the value of $y$ for the quadratic function $y = -x^2 + 6x - 5$ when $x = 0.5$ .

Solve the linear equation $x=-x+2$ for the value of $x$ .

Publish a book: $25x + 1100 = y$ . Find the startup cost and cost change per book.

Subtract $\frac{1}{2}(x-4)(x-2)$ from $5x+10$ and simplify to $6+8x-\frac{1}{2}x^2$ .

Find the difference between the perimeters $P_1$ and $P_2$ of two figures, where the difference is $n$ . Write and solve an absolute value inequality to represent the situation.

Find the value of $x$ given the equation $3x + 2 = 8$ .

Find the value of $g$ that satisfies the inequality $9 + 5g > -1$ .

Find the property described by the statement: "If $a=b$ , then either $a$ or $b$ may be the other in any equation."

Solve the absolute value equation $|7x-5| = 39$ by finding two possible values for $7x-5$ .

Solve the system of linear inequalities: $5x < -20$ and $3x > 12$ .

Describe the transformation of the linear function $f(x) = \frac{1}{3}x$ .