Solved on Jan 19, 2024

Solve the linear equation $-x-2(9-8x)=12$ for the unknown variable $x$ .

STEP 1

Assumptions
1. We are given the equation $-x - 2(9 - 8x) = 12$ .
2. We need to solve for the variable $x$ .

STEP 2

First, we need to distribute the $-2$ across the terms inside the parentheses.
$-x - 2 \cdot 9 + 2 \cdot 8x = 12$

STEP 3

Perform the multiplication.
$-x - 18 + 16x = 12$

STEP 4

Combine like terms on the left side of the equation.
$16x - x - 18 = 12$

STEP 5

Simplify the left side by combining the $x$ terms.
$(16 - 1)x - 18 = 12$

STEP 6

Further simplify the left side.
$15x - 18 = 12$

STEP 7

Now, we need to isolate the variable $x$ on one side. First, add $18$ to both sides of the equation to move the constant term to the right side.
$15x - 18 + 18 = 12 + 18$

STEP 8

Simplify both sides of the equation.
$15x = 30$

STEP 9

To find the value of $x$ , divide both sides of the equation by $15$ .
$\frac{15x}{15} = \frac{30}{15}$

STEP 10

Simplify the equation to find the value of $x$ .
$x = 2$
The solution to the equation $-x - 2(9 - 8x) = 12$ is $x = 2$ .

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Solve the linear equation $-x-2(9-8x)=12$ for the unknown variable $x$ .

STEP 1

Assumptions
1. We are given the equation $-x - 2(9 - 8x) = 12$ .
2. We need to solve for the variable $x$ .

STEP 2

First, we need to distribute the $-2$ across the terms inside the parentheses.
$-x - 2 \cdot 9 + 2 \cdot 8x = 12$

STEP 3

Perform the multiplication.
$-x - 18 + 16x = 12$

STEP 4

Combine like terms on the left side of the equation.
$16x - x - 18 = 12$

STEP 5

Simplify the left side by combining the $x$ terms.
$(16 - 1)x - 18 = 12$

STEP 6

Further simplify the left side.
$15x - 18 = 12$

STEP 7

Now, we need to isolate the variable $x$ on one side. First, add $18$ to both sides of the equation to move the constant term to the right side.
$15x - 18 + 18 = 12 + 18$

STEP 8

Simplify both sides of the equation.
$15x = 30$

STEP 9

To find the value of $x$ , divide both sides of the equation by $15$ .
$\frac{15x}{15} = \frac{30}{15}$

STEP 10

Simplify the equation to find the value of $x$ .
$x = 2$
The solution to the equation $-x - 2(9 - 8x) = 12$ is $x = 2$ .

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Solve the linear equation −x−2(9−8x)=12-x-2(9-8x)=12−x−2(9−8x)=12 for the unknown variable xxx.

STEP 1

Assumptions1. We are given the equation −x−2(9−8x)=12-x - 2(9 - 8x) = 12−x−2(9−8x)=12.2. We need to solve for the variable xxx.

STEP 2

First, we need to distribute the −2-2−2 across the terms inside the parentheses.−x−2⋅9+2⋅8x=12-x - 2 \cdot 9 + 2 \cdot 8x = 12−x−2⋅9+2⋅8x=12

STEP 3

Perform the multiplication.−x−18+16x=12-x - 18 + 16x = 12−x−18+16x=12

STEP 4

Combine like terms on the left side of the equation.16x−x−18=1216x - x - 18 = 1216x−x−18=12

STEP 5

Simplify the left side by combining the xxx terms.(16−1)x−18=12(16 - 1)x - 18 = 12(16−1)x−18=12

STEP 6

Further simplify the left side.15x−18=1215x - 18 = 1215x−18=12

STEP 7

Now, we need to isolate the variable xxx on one side. First, add 181818 to both sides of the equation to move the constant term to the right side.15x−18+18=12+1815x - 18 + 18 = 12 + 1815x−18+18=12+18

STEP 8

Simplify both sides of the equation.15x=3015x = 3015x=30

STEP 9

To find the value of xxx, divide both sides of the equation by 151515.15x15=3015\frac{15x}{15} = \frac{30}{15}1515x​=1530​

STEP 10

Simplify the equation to find the value of xxx.x=2x = 2x=2The solution to the equation −x−2(9−8x)=12-x - 2(9 - 8x) = 12−x−2(9−8x)=12 is x=2x = 2x=2.

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

Solve the linear equation $-x-2(9-8x)=12$ for the unknown variable $x$ .

Assumptions
1. We are given the equation $-x - 2(9 - 8x) = 12$ .
2. We need to solve for the variable $x$ .

First, we need to distribute the $-2$ across the terms inside the parentheses.
$-x - 2 \cdot 9 + 2 \cdot 8x = 12$

Perform the multiplication.
$-x - 18 + 16x = 12$

Combine like terms on the left side of the equation.
$16x - x - 18 = 12$

Simplify the left side by combining the $x$ terms.
$(16 - 1)x - 18 = 12$

Further simplify the left side.
$15x - 18 = 12$

Now, we need to isolate the variable $x$ on one side. First, add $18$ to both sides of the equation to move the constant term to the right side.
$15x - 18 + 18 = 12 + 18$

Simplify both sides of the equation.
$15x = 30$

To find the value of $x$ , divide both sides of the equation by $15$ .
$\frac{15x}{15} = \frac{30}{15}$

Simplify the equation to find the value of $x$ .
$x = 2$
The solution to the equation $-x - 2(9 - 8x) = 12$ is $x = 2$ .