Algebra Examples

$12 (9 - 3 x) + 2 x = 516$

Step 1

Simplify $12 (9 - 3 x) + 2 x$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the distributive property.

$12 \cdot 9 + 12 (- 3 x) + 2 x = 516$

Step 1.1.2

Multiply $12$ by $9$ .

$108 + 12 (- 3 x) + 2 x = 516$

Step 1.1.3

Multiply $- 3$ by $12$ .

$108 - 36 x + 2 x = 516$

Step 1.2

Add $- 36 x$ and $2 x$ .

$108 - 34 x = 516$

Step 2

Move all terms not containing $x$ to the right side of the equation.

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Step 2.1

Subtract $108$ from both sides of the equation.

$- 34 x = 516 - 108$

Step 2.2

Subtract $108$ from $516$ .

$- 34 x = 408$

Step 3

Divide each term in $- 34 x = 408$ by $- 34$ and simplify.

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Step 3.1

Divide each term in $- 34 x = 408$ by $- 34$ .

$\frac{- 34 x}{- 34} = \frac{408}{- 34}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 34$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 34 x}{- 34} = \frac{408}{- 34}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{408}{- 34}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $408$ by $- 34$ .

$x = - 12$