Pre-Algebra Examples

$\frac{1}{2} \cdot (16 - x) = - 12 (x + 7)$

Step 1

Simplify $\frac{1}{2} \cdot (16 - x)$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{1}{2} \cdot (16 - x) = - 12 (x + 7)$

Step 1.2

Simplify by adding zeros.

$\frac{1}{2} \cdot (16 - x) = - 12 (x + 7)$

Step 1.3

Apply the distributive property.

$\frac{1}{2} \cdot 16 + \frac{1}{2} (- x) = - 12 (x + 7)$

Step 1.4

Cancel the common factor of $2$ .

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Step 1.4.1

Factor $2$ out of $16$ .

$\frac{1}{2} \cdot (2 (8)) + \frac{1}{2} (- x) = - 12 (x + 7)$

Step 1.4.2

Cancel the common factor.

$\frac{1}{2} \cdot (2 \cdot 8) + \frac{1}{2} (- x) = - 12 (x + 7)$

Step 1.4.3

Rewrite the expression.

$8 + \frac{1}{2} (- x) = - 12 (x + 7)$

Step 1.5

Combine $\frac{1}{2}$ and $x$ .

$8 - \frac{x}{2} = - 12 (x + 7)$

Step 2

Simplify $- 12 (x + 7)$ .

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Step 2.1

Apply the distributive property.

$8 - \frac{x}{2} = - 12 x - 12 \cdot 7$

Step 2.2

Multiply $- 12$ by $7$ .

$8 - \frac{x}{2} = - 12 x - 84$

Step 3

Move all terms containing $x$ to the left side of the equation.

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Step 3.1

Add $12 x$ to both sides of the equation.

$8 - \frac{x}{2} + 12 x = - 84$

Step 3.2

To write $12 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$8 - \frac{x}{2} + 12 x \cdot \frac{2}{2} = - 84$

Step 3.3

Combine $12 x$ and $\frac{2}{2}$ .

$8 - \frac{x}{2} + \frac{12 x \cdot 2}{2} = - 84$

Step 3.4

Combine the numerators over the common denominator.

$8 + \frac{- x + 12 x \cdot 2}{2} = - 84$

Step 3.5

Simplify each term.

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Step 3.5.1

Simplify the numerator.

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Step 3.5.1.1

Factor $x$ out of $- x + 12 x \cdot 2$ .

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Step 3.5.1.1.1

Factor $x$ out of $- x$ .

$8 + \frac{x \cdot - 1 + 12 x \cdot 2}{2} = - 84$

Step 3.5.1.1.2

Factor $x$ out of $12 x \cdot 2$ .

$8 + \frac{x \cdot - 1 + x (12 \cdot 2)}{2} = - 84$

Step 3.5.1.1.3

Factor $x$ out of $x \cdot - 1 + x (12 \cdot 2)$ .

$8 + \frac{x (- 1 + 12 \cdot 2)}{2} = - 84$

Step 3.5.1.2

Multiply $12$ by $2$ .

$8 + \frac{x (- 1 + 24)}{2} = - 84$

Step 3.5.1.3

Add $- 1$ and $24$ .

$8 + \frac{x \cdot 23}{2} = - 84$

Step 3.5.2

Move $23$ to the left of $x$ .

$8 + \frac{23 x}{2} = - 84$

Step 4

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

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Step 4.1

Subtract $8$ from both sides of the equation.

$\frac{23 x}{2} = - 84 - 8$

Step 4.2

Subtract $8$ from $- 84$ .

$\frac{23 x}{2} = - 92$

Step 5

Multiply both sides of the equation by $\frac{2}{23}$ .

$\frac{2}{23} \cdot \frac{23 x}{2} = \frac{2}{23} \cdot - 92$

Step 6

Simplify both sides of the equation.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Simplify $\frac{2}{23} \cdot \frac{23 x}{2}$ .

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Step 6.1.1.1

Cancel the common factor of $2$ .

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Step 6.1.1.1.1

Cancel the common factor.

$\frac{2}{23} \cdot \frac{23 x}{2} = \frac{2}{23} \cdot - 92$

Step 6.1.1.1.2

Rewrite the expression.

$\frac{1}{23} (23 x) = \frac{2}{23} \cdot - 92$

Step 6.1.1.2

Cancel the common factor of $23$ .

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Step 6.1.1.2.1

Factor $23$ out of $23 x$ .

$\frac{1}{23} (23 (x)) = \frac{2}{23} \cdot - 92$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{1}{23} (23 x) = \frac{2}{23} \cdot - 92$

Step 6.1.1.2.3

Rewrite the expression.

$x = \frac{2}{23} \cdot - 92$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $\frac{2}{23} \cdot - 92$ .

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Step 6.2.1.1

Cancel the common factor of $23$ .

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Step 6.2.1.1.1

Factor $23$ out of $- 92$ .

$x = \frac{2}{23} \cdot (23 (- 4))$

Step 6.2.1.1.2

Cancel the common factor.

$x = \frac{2}{23} \cdot (23 \cdot - 4)$

Step 6.2.1.1.3

Rewrite the expression.

$x = 2 \cdot - 4$

Step 6.2.1.2

Multiply $2$ by $- 4$ .

$x = - 8$