Algebra Examples

$\frac{16 - 2 x}{- 4} = 9$

Step 1

Cancel the common factor of $16 - 2 x$ and $- 4$ .

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Step 1.1

Factor $2$ out of $16$ .

$\frac{2 (8) - 2 x}{- 4} = 9$

Step 1.2

Factor $2$ out of $- 2 x$ .

$\frac{2 (8) + 2 (- x)}{- 4} = 9$

Step 1.3

Factor $2$ out of $2 (8) + 2 (- x)$ .

$\frac{2 (8 - x)}{- 4} = 9$

Step 1.4

Cancel the common factors.

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Step 1.4.1

Factor $2$ out of $- 4$ .

$\frac{2 (8 - x)}{2 \cdot - 2} = 9$

Step 1.4.2

Cancel the common factor.

$\frac{2 (8 - x)}{2 \cdot - 2} = 9$

Step 1.4.3

Rewrite the expression.

$\frac{8 - x}{- 2} = 9$

Step 2

Multiply both sides by $- 2$ .

$\frac{8 - x}{- 2} \cdot - 2 = 9 \cdot - 2$

Step 3

Simplify.

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Step 3.1

Simplify the left side.

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Step 3.1.1

Simplify $\frac{8 - x}{- 2} \cdot - 2$ .

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Step 3.1.1.1

Cancel the common factor of $2$ .

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Step 3.1.1.1.1

Factor $2$ out of $- 2$ .

$\frac{8 - x}{2 (- 1)} \cdot - 2 = 9 \cdot - 2$

Step 3.1.1.1.2

Factor $2$ out of $- 2$ .

$\frac{8 - x}{2 \cdot - 1} \cdot (2 \cdot - 1) = 9 \cdot - 2$

Step 3.1.1.1.3

Cancel the common factor.

$\frac{8 - x}{2 \cdot - 1} \cdot (2 \cdot - 1) = 9 \cdot - 2$

Step 3.1.1.1.4

Rewrite the expression.

$\frac{8 - x}{- 1} \cdot - 1 = 9 \cdot - 2$

Step 3.1.1.2

Combine $\frac{8 - x}{- 1}$ and $- 1$ .

$\frac{(8 - x) \cdot - 1}{- 1} = 9 \cdot - 2$

Step 3.1.1.3

Simplify the expression.

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Step 3.1.1.3.1

Move the negative one from the denominator of $\frac{(8 - x) \cdot - 1}{- 1}$ .

$- 1 \cdot ((8 - x) \cdot - 1) = 9 \cdot - 2$

Step 3.1.1.3.2

Rewrite $- 1 \cdot ((8 - x) \cdot - 1)$ as $- ((8 - x) \cdot - 1)$ .

$- ((8 - x) \cdot - 1) = 9 \cdot - 2$

Step 3.1.1.4

Apply the distributive property.

$- (8 \cdot - 1 - x \cdot - 1) = 9 \cdot - 2$

Step 3.1.1.5

Multiply $8$ by $- 1$ .

$- (- 8 - x \cdot - 1) = 9 \cdot - 2$

Step 3.1.1.6

Multiply $- x \cdot - 1$ .

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Step 3.1.1.6.1

Multiply $- 1$ by $- 1$ .

$- (- 8 + 1 x) = 9 \cdot - 2$

Step 3.1.1.6.2

Multiply $x$ by $1$ .

$- (- 8 + x) = 9 \cdot - 2$

Step 3.1.1.7

Apply the distributive property.

$- - 8 - x = 9 \cdot - 2$

Step 3.1.1.8

Simplify the expression.

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Step 3.1.1.8.1

Multiply $- 1$ by $- 8$ .

$8 - x = 9 \cdot - 2$

Step 3.1.1.8.2

Reorder $8$ and $- x$ .

$- x + 8 = 9 \cdot - 2$

Step 3.2

Simplify the right side.

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Step 3.2.1

Multiply $9$ by $- 2$ .

$- x + 8 = - 18$

Step 4

Solve for $x$ .

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Step 4.1

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

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Step 4.1.1

Subtract $8$ from both sides of the equation.

$- x = - 18 - 8$

Step 4.1.2

Subtract $8$ from $- 18$ .

$- x = - 26$

Step 4.2

Divide each term in $- x = - 26$ by $- 1$ and simplify.

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Step 4.2.1

Divide each term in $- x = - 26$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 26}{- 1}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 26}{- 1}$

Step 4.2.2.2

Divide $x$ by $1$ .

$x = \frac{- 26}{- 1}$

Step 4.2.3

Simplify the right side.

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Step 4.2.3.1

Divide $- 26$ by $- 1$ .

$x = 26$