Pre-Algebra Examples

$\frac{1}{10} \cdot (x + 11) = - 2 (8 - x)$

Step 1

Simplify $\frac{1}{10} \cdot (x + 11)$ .

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Step 1.1

Rewrite.

$0 + 0 + \frac{1}{10} \cdot (x + 11) = - 2 (8 - x)$

Step 1.2

Simplify by adding zeros.

$\frac{1}{10} \cdot (x + 11) = - 2 (8 - x)$

Step 1.3

Apply the distributive property.

$\frac{1}{10} x + \frac{1}{10} \cdot 11 = - 2 (8 - x)$

Step 1.4

Combine $\frac{1}{10}$ and $x$ .

$\frac{x}{10} + \frac{1}{10} \cdot 11 = - 2 (8 - x)$

Step 1.5

Combine $\frac{1}{10}$ and $11$ .

$\frac{x}{10} + \frac{11}{10} = - 2 (8 - x)$

Step 2

Simplify $- 2 (8 - x)$ .

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Step 2.1

Apply the distributive property.

$\frac{x}{10} + \frac{11}{10} = - 2 \cdot 8 - 2 (- x)$

Step 2.2

Multiply.

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Step 2.2.1

Multiply $- 2$ by $8$ .

$\frac{x}{10} + \frac{11}{10} = - 16 - 2 (- x)$

Step 2.2.2

Multiply $- 1$ by $- 2$ .

$\frac{x}{10} + \frac{11}{10} = - 16 + 2 x$

Step 3

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

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Step 3.1

Subtract $2 x$ from both sides of the equation.

$\frac{x}{10} + \frac{11}{10} - 2 x = - 16$

Step 3.2

To write $- 2 x$ as a fraction with a common denominator, multiply by $\frac{10}{10}$ .

$\frac{x}{10} - 2 x \cdot \frac{10}{10} + \frac{11}{10} = - 16$

Step 3.3

Combine $- 2 x$ and $\frac{10}{10}$ .

$\frac{x}{10} + \frac{- 2 x \cdot 10}{10} + \frac{11}{10} = - 16$

Step 3.4

Combine the numerators over the common denominator.

$\frac{x - 2 x \cdot 10}{10} + \frac{11}{10} = - 16$

Step 3.5

Combine the numerators over the common denominator.

$\frac{x - 2 x \cdot 10 + 11}{10} = - 16$

Step 3.6

Multiply $10$ by $- 2$ .

$\frac{x - 20 x + 11}{10} = - 16$

Step 3.7

Subtract $20 x$ from $x$ .

$\frac{- 19 x + 11}{10} = - 16$

Step 3.8

Factor $- 1$ out of $- 19 x$ .

$\frac{- (19 x) + 11}{10} = - 16$

Step 3.9

Rewrite $11$ as $- 1 (- 11)$ .

$\frac{- (19 x) - 1 (- 11)}{10} = - 16$

Step 3.10

Factor $- 1$ out of $- (19 x) - 1 (- 11)$ .

$\frac{- (19 x - 11)}{10} = - 16$

Step 3.11

Rewrite $- (19 x - 11)$ as $- 1 (19 x - 11)$ .

$\frac{- 1 (19 x - 11)}{10} = - 16$

Step 3.12

Move the negative in front of the fraction.

$- \frac{19 x - 11}{10} = - 16$

Step 4

Multiply both sides of the equation by $- 10$ .

$- 10 (- \frac{19 x - 11}{10}) = - 10 \cdot - 16$

Step 5

Simplify both sides of the equation.

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Step 5.1

Simplify the left side.

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Step 5.1.1

Simplify $- 10 (- \frac{19 x - 11}{10})$ .

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Step 5.1.1.1

Cancel the common factor of $10$ .

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Step 5.1.1.1.1

Move the leading negative in $- \frac{19 x - 11}{10}$ into the numerator.

$- 10 \frac{- (19 x - 11)}{10} = - 10 \cdot - 16$

Step 5.1.1.1.2

Factor $10$ out of $- 10$ .

$10 (- 1) \frac{- (19 x - 11)}{10} = - 10 \cdot - 16$

Step 5.1.1.1.3

Cancel the common factor.

$10 \cdot - 1 \frac{- (19 x - 11)}{10} = - 10 \cdot - 16$

Step 5.1.1.1.4

Rewrite the expression.

$- - (19 x - 11) = - 10 \cdot - 16$

Step 5.1.1.2

Multiply.

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Step 5.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 (19 x - 11) = - 10 \cdot - 16$

Step 5.1.1.2.2

Multiply $19 x - 11$ by $1$ .

$19 x - 11 = - 10 \cdot - 16$

Step 5.2

Simplify the right side.

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Step 5.2.1

Multiply $- 10$ by $- 16$ .

$19 x - 11 = 160$

Step 6

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

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Step 6.1

Add $11$ to both sides of the equation.

$19 x = 160 + 11$

Step 6.2

Add $160$ and $11$ .

$19 x = 171$

Step 7

Divide each term in $19 x = 171$ by $19$ and simplify.

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Step 7.1

Divide each term in $19 x = 171$ by $19$ .

$\frac{19 x}{19} = \frac{171}{19}$

Step 7.2

Simplify the left side.

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Step 7.2.1

Cancel the common factor of $19$ .

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Step 7.2.1.1

Cancel the common factor.

$\frac{19 x}{19} = \frac{171}{19}$

Step 7.2.1.2

Divide $x$ by $1$ .

$x = \frac{171}{19}$

Step 7.3

Simplify the right side.

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Step 7.3.1

Divide $171$ by $19$ .

$x = 9$