Pre-Algebra Examples

$\frac{- 1}{7} \cdot (x - 11) = 2$

Step 1

Multiply both sides of the equation by $\frac{7}{- 1}$ .

$\frac{7}{- 1} (\frac{- 1}{7} \cdot (x - 11)) = \frac{7}{- 1} \cdot 2$

Step 2

Simplify both sides of the equation.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{7}{- 1} (\frac{- 1}{7} \cdot (x - 11))$ .

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Step 2.1.1.1

Simplify the expression.

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Step 2.1.1.1.1

Divide $7$ by $- 1$ .

$- 7 (\frac{- 1}{7} \cdot (x - 11)) = \frac{7}{- 1} \cdot 2$

Step 2.1.1.1.2

Move the negative in front of the fraction.

$- 7 (- \frac{1}{7} \cdot (x - 11)) = \frac{7}{- 1} \cdot 2$

Step 2.1.1.2

Apply the distributive property.

$- 7 (- \frac{1}{7} x - \frac{1}{7} \cdot - 11) = \frac{7}{- 1} \cdot 2$

Step 2.1.1.3

Combine $x$ and $\frac{1}{7}$ .

$- 7 (- \frac{x}{7} - \frac{1}{7} \cdot - 11) = \frac{7}{- 1} \cdot 2$

Step 2.1.1.4

Multiply $- \frac{1}{7} \cdot - 11$ .

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Step 2.1.1.4.1

Multiply $- 11$ by $- 1$ .

$- 7 (- \frac{x}{7} + 11 (\frac{1}{7})) = \frac{7}{- 1} \cdot 2$

Step 2.1.1.4.2

Combine $11$ and $\frac{1}{7}$ .

$- 7 (- \frac{x}{7} + \frac{11}{7}) = \frac{7}{- 1} \cdot 2$

Step 2.1.1.5

Apply the distributive property.

$- 7 (- \frac{x}{7}) - 7 (\frac{11}{7}) = \frac{7}{- 1} \cdot 2$

Step 2.1.1.6

Cancel the common factor of $7$ .

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Step 2.1.1.6.1

Move the leading negative in $- \frac{x}{7}$ into the numerator.

$- 7 \frac{- x}{7} - 7 (\frac{11}{7}) = \frac{7}{- 1} \cdot 2$

Step 2.1.1.6.2

Factor $7$ out of $- 7$ .

$7 (- 1) \frac{- x}{7} - 7 (\frac{11}{7}) = \frac{7}{- 1} \cdot 2$

Step 2.1.1.6.3

Cancel the common factor.

$7 \cdot - 1 \frac{- x}{7} - 7 (\frac{11}{7}) = \frac{7}{- 1} \cdot 2$

Step 2.1.1.6.4

Rewrite the expression.

$- - x - 7 (\frac{11}{7}) = \frac{7}{- 1} \cdot 2$

Step 2.1.1.7

Multiply.

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Step 2.1.1.7.1

Multiply $- 1$ by $- 1$ .

$1 x - 7 (\frac{11}{7}) = \frac{7}{- 1} \cdot 2$

Step 2.1.1.7.2

Multiply $x$ by $1$ .

$x - 7 (\frac{11}{7}) = \frac{7}{- 1} \cdot 2$

Step 2.1.1.8

Cancel the common factor of $7$ .

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Step 2.1.1.8.1

Factor $7$ out of $- 7$ .

$x + 7 (- 1) \frac{11}{7} = \frac{7}{- 1} \cdot 2$

Step 2.1.1.8.2

Cancel the common factor.

$x + 7 \cdot - 1 \frac{11}{7} = \frac{7}{- 1} \cdot 2$

Step 2.1.1.8.3

Rewrite the expression.

$x - 1 \cdot 11 = \frac{7}{- 1} \cdot 2$

Step 2.1.1.9

Multiply $- 1$ by $11$ .

$x - 11 = \frac{7}{- 1} \cdot 2$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $\frac{7}{- 1} \cdot 2$ .

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Step 2.2.1.1

Divide $7$ by $- 1$ .

$x - 11 = - 7 \cdot 2$

Step 2.2.1.2

Multiply $- 7$ by $2$ .

$x - 11 = - 14$

Step 3

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

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Step 3.1

Add $11$ to both sides of the equation.

$x = - 14 + 11$

Step 3.2

Add $- 14$ and $11$ .

$x = - 3$