Solved on Jan 21, 2024

Solve linear equations with one or two variables. Find the value of an expression given a value for the variable.
a. Solve: $5x+2=10$ b. Find $5x+2$ when $x=-3$ c. Solve for $y: 5x+2y=10$ d. Solve for $x: 5x+2y=10$

STEP 1

Assumptions
1. For part a, we are solving a linear equation in one variable.
2. For part b, we are evaluating an expression for a given value of $x$ .
3. For part c, we are solving a linear equation in two variables for $y$ .
4. For part d, we are solving a linear equation in two variables for $x$ .

STEP 2

Solve for $x$ in the equation $5x + 2 = 10$ .
First, subtract 2 from both sides of the equation to isolate the term with $x$ .
$5x + 2 - 2 = 10 - 2$

STEP 3

Simplify both sides of the equation.
$5x = 8$

STEP 4

Now, divide both sides by 5 to solve for $x$ .
$\frac{5x}{5} = \frac{8}{5}$

STEP 5

Simplify the equation to find the value of $x$ .
$x = \frac{8}{5}$
For part a, $x = \frac{8}{5}$ .

STEP 6

For part b, find the value of $5x + 2$ when $x = -3$ .
Substitute $x$ with $-3$ in the expression $5x + 2$ .
$5(-3) + 2$

STEP 7

Perform the multiplication and addition to evaluate the expression.
$-15 + 2$

STEP 8

Simplify the expression to find the value.
$-15 + 2 = -13$
For part b, $5x + 2 = -13$ when $x = -3$ .

STEP 9

For part c, solve for $y$ in the equation $5x + 2y = 10$ .
We can solve for $y$ by first isolating the term with $y$ .
Subtract $5x$ from both sides of the equation.
$5x + 2y - 5x = 10 - 5x$

STEP 10

Simplify both sides of the equation.
$2y = 10 - 5x$

STEP 11

Now, divide both sides by 2 to solve for $y$ .
$\frac{2y}{2} = \frac{10 - 5x}{2}$

STEP 12

Simplify the equation to find the value of $y$ .
$y = \frac{10 - 5x}{2}$
For part c, $y = \frac{10 - 5x}{2}$ .

STEP 13

For part d, solve for $x$ in the equation $5x + 2y = 10$ .
We can solve for $x$ by first isolating the term with $x$ .
Subtract $2y$ from both sides of the equation.
$5x + 2y - 2y = 10 - 2y$

STEP 14

Simplify both sides of the equation.
$5x = 10 - 2y$

STEP 15

Now, divide both sides by 5 to solve for $x$ .
$\frac{5x}{5} = \frac{10 - 2y}{5}$

STEP 16

Simplify the equation to find the value of $x$ .
$x = \frac{10 - 2y}{5}$
For part d, $x = \frac{10 - 2y}{5}$ .

Was this helpful?

Solve linear equations with one or two variables. Find the value of an expression given a value for the variable.
a. Solve: $5x+2=10$ b. Find $5x+2$ when $x=-3$ c. Solve for $y: 5x+2y=10$ d. Solve for $x: 5x+2y=10$

STEP 1

Assumptions
1. For part a, we are solving a linear equation in one variable.
2. For part b, we are evaluating an expression for a given value of $x$ .
3. For part c, we are solving a linear equation in two variables for $y$ .
4. For part d, we are solving a linear equation in two variables for $x$ .

STEP 2

Solve for $x$ in the equation $5x + 2 = 10$ .
First, subtract 2 from both sides of the equation to isolate the term with $x$ .
$5x + 2 - 2 = 10 - 2$

STEP 3

Simplify both sides of the equation.
$5x = 8$

STEP 4

Now, divide both sides by 5 to solve for $x$ .
$\frac{5x}{5} = \frac{8}{5}$

STEP 5

Simplify the equation to find the value of $x$ .
$x = \frac{8}{5}$
For part a, $x = \frac{8}{5}$ .

STEP 6

For part b, find the value of $5x + 2$ when $x = -3$ .
Substitute $x$ with $-3$ in the expression $5x + 2$ .
$5(-3) + 2$

STEP 7

Perform the multiplication and addition to evaluate the expression.
$-15 + 2$

STEP 8

Simplify the expression to find the value.
$-15 + 2 = -13$
For part b, $5x + 2 = -13$ when $x = -3$ .

STEP 9

For part c, solve for $y$ in the equation $5x + 2y = 10$ .
We can solve for $y$ by first isolating the term with $y$ .
Subtract $5x$ from both sides of the equation.
$5x + 2y - 5x = 10 - 5x$

STEP 10

Simplify both sides of the equation.
$2y = 10 - 5x$

STEP 11

Now, divide both sides by 2 to solve for $y$ .
$\frac{2y}{2} = \frac{10 - 5x}{2}$

STEP 12

Simplify the equation to find the value of $y$ .
$y = \frac{10 - 5x}{2}$
For part c, $y = \frac{10 - 5x}{2}$ .

STEP 13

For part d, solve for $x$ in the equation $5x + 2y = 10$ .
We can solve for $x$ by first isolating the term with $x$ .
Subtract $2y$ from both sides of the equation.
$5x + 2y - 2y = 10 - 2y$

STEP 14

Simplify both sides of the equation.
$5x = 10 - 2y$

STEP 15

Now, divide both sides by 5 to solve for $x$ .
$\frac{5x}{5} = \frac{10 - 2y}{5}$

STEP 16

Simplify the equation to find the value of $x$ .
$x = \frac{10 - 2y}{5}$
For part d, $x = \frac{10 - 2y}{5}$ .

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Solve linear equations with one or two variables. Find the value of an expression given a value for the variable.a. Solve: 5x+2=105x+2=105x+2=10 b. Find 5x+25x+25x+2 when x=−3x=-3x=−3 c. Solve for y:5x+2y=10y: 5x+2y=10y:5x+2y=10 d. Solve for x:5x+2y=10x: 5x+2y=10x:5x+2y=10

STEP 1

Assumptions1. For part a, we are solving a linear equation in one variable.2. For part b, we are evaluating an expression for a given value of xxx.3. For part c, we are solving a linear equation in two variables for yyy.4. For part d, we are solving a linear equation in two variables for xxx.

STEP 2

Solve for xxx in the equation 5x+2=105x + 2 = 105x+2=10.First, subtract 2 from both sides of the equation to isolate the term with xxx.5x+2−2=10−25x + 2 - 2 = 10 - 25x+2−2=10−2

STEP 3

Simplify both sides of the equation.5x=85x = 85x=8

STEP 4

Now, divide both sides by 5 to solve for xxx.5x5=85\frac{5x}{5} = \frac{8}{5}55x​=58​

STEP 5

Simplify the equation to find the value of xxx.x=85x = \frac{8}{5}x=58​For part a, x=85x = \frac{8}{5}x=58​.

STEP 6

For part b, find the value of 5x+25x + 25x+2 when x=−3x = -3x=−3.Substitute xxx with −3-3−3 in the expression 5x+25x + 25x+2.5(−3)+25(-3) + 25(−3)+2

STEP 7

Perform the multiplication and addition to evaluate the expression.−15+2-15 + 2−15+2

STEP 8

Simplify the expression to find the value.−15+2=−13-15 + 2 = -13−15+2=−13For part b, 5x+2=−135x + 2 = -135x+2=−13 when x=−3x = -3x=−3.

STEP 9

For part c, solve for yyy in the equation 5x+2y=105x + 2y = 105x+2y=10.We can solve for yyy by first isolating the term with yyy.Subtract 5x5x5x from both sides of the equation.5x+2y−5x=10−5x5x + 2y - 5x = 10 - 5x5x+2y−5x=10−5x

STEP 10

Simplify both sides of the equation.2y=10−5x2y = 10 - 5x2y=10−5x

STEP 11

Now, divide both sides by 2 to solve for yyy.2y2=10−5x2\frac{2y}{2} = \frac{10 - 5x}{2}22y​=210−5x​

STEP 12

Simplify the equation to find the value of yyy.y=10−5x2y = \frac{10 - 5x}{2}y=210−5x​For part c, y=10−5x2y = \frac{10 - 5x}{2}y=210−5x​.

STEP 13

For part d, solve for xxx in the equation 5x+2y=105x + 2y = 105x+2y=10.We can solve for xxx by first isolating the term with xxx.Subtract 2y2y2y from both sides of the equation.5x+2y−2y=10−2y5x + 2y - 2y = 10 - 2y5x+2y−2y=10−2y

STEP 14

Simplify both sides of the equation.5x=10−2y5x = 10 - 2y5x=10−2y

STEP 15

Now, divide both sides by 5 to solve for xxx.5x5=10−2y5\frac{5x}{5} = \frac{10 - 2y}{5}55x​=510−2y​

STEP 16

Simplify the equation to find the value of xxx.x=10−2y5x = \frac{10 - 2y}{5}x=510−2y​For part d, x=10−2y5x = \frac{10 - 2y}{5}x=510−2y​.

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Solve linear equations with one or two variables. Find the value of an expression given a value for the variable.
a. Solve: $5x+2=10$ b. Find $5x+2$ when $x=-3$ c. Solve for $y: 5x+2y=10$ d. Solve for $x: 5x+2y=10$

Solve for $x$ in the equation $5x + 2 = 10$ .
First, subtract 2 from both sides of the equation to isolate the term with $x$ .
$5x + 2 - 2 = 10 - 2$

Simplify both sides of the equation.
$5x = 8$

Now, divide both sides by 5 to solve for $x$ .
$\frac{5x}{5} = \frac{8}{5}$

Simplify the equation to find the value of $x$ .
$x = \frac{8}{5}$
For part a, $x = \frac{8}{5}$ .

For part b, find the value of $5x + 2$ when $x = -3$ .
Substitute $x$ with $-3$ in the expression $5x + 2$ .
$5(-3) + 2$

Perform the multiplication and addition to evaluate the expression.
$-15 + 2$

Simplify the expression to find the value.
$-15 + 2 = -13$
For part b, $5x + 2 = -13$ when $x = -3$ .

For part c, solve for $y$ in the equation $5x + 2y = 10$ .
We can solve for $y$ by first isolating the term with $y$ .
Subtract $5x$ from both sides of the equation.
$5x + 2y - 5x = 10 - 5x$

Simplify both sides of the equation.
$2y = 10 - 5x$

Now, divide both sides by 2 to solve for $y$ .
$\frac{2y}{2} = \frac{10 - 5x}{2}$

Simplify the equation to find the value of $y$ .
$y = \frac{10 - 5x}{2}$
For part c, $y = \frac{10 - 5x}{2}$ .

For part d, solve for $x$ in the equation $5x + 2y = 10$ .
We can solve for $x$ by first isolating the term with $x$ .
Subtract $2y$ from both sides of the equation.
$5x + 2y - 2y = 10 - 2y$

Simplify both sides of the equation.
$5x = 10 - 2y$

Now, divide both sides by 5 to solve for $x$ .
$\frac{5x}{5} = \frac{10 - 2y}{5}$

Simplify the equation to find the value of $x$ .
$x = \frac{10 - 2y}{5}$
For part d, $x = \frac{10 - 2y}{5}$ .