Algebra Examples

$- \frac{1}{2} (x + 5) = - 10$

Step 1

Multiply both sides of the equation by $- 2$ .

$- 2 (- \frac{1}{2} \cdot (x + 5)) = - 2 \cdot - 10$

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 $- 2 (- \frac{1}{2} \cdot (x + 5))$ .

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Step 2.1.1.1

Apply the distributive property.

$- 2 (- \frac{1}{2} x - \frac{1}{2} \cdot 5) = - 2 \cdot - 10$

Step 2.1.1.2

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

$- 2 (- \frac{x}{2} - \frac{1}{2} \cdot 5) = - 2 \cdot - 10$

Step 2.1.1.3

Multiply $- \frac{1}{2} \cdot 5$ .

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Step 2.1.1.3.1

Multiply $5$ by $- 1$ .

$- 2 (- \frac{x}{2} - 5 (\frac{1}{2})) = - 2 \cdot - 10$

Step 2.1.1.3.2

Combine $- 5$ and $\frac{1}{2}$ .

$- 2 (- \frac{x}{2} + \frac{- 5}{2}) = - 2 \cdot - 10$

Step 2.1.1.4

Move the negative in front of the fraction.

$- 2 (- \frac{x}{2} - \frac{5}{2}) = - 2 \cdot - 10$

Step 2.1.1.5

Apply the distributive property.

$- 2 (- \frac{x}{2}) - 2 (- \frac{5}{2}) = - 2 \cdot - 10$

Step 2.1.1.6

Cancel the common factor of $2$ .

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Step 2.1.1.6.1

Move the leading negative in $- \frac{x}{2}$ into the numerator.

$- 2 \frac{- x}{2} - 2 (- \frac{5}{2}) = - 2 \cdot - 10$

Step 2.1.1.6.2

Factor $2$ out of $- 2$ .

$2 (- 1) \frac{- x}{2} - 2 (- \frac{5}{2}) = - 2 \cdot - 10$

Step 2.1.1.6.3

Cancel the common factor.

$2 \cdot - 1 \frac{- x}{2} - 2 (- \frac{5}{2}) = - 2 \cdot - 10$

Step 2.1.1.6.4

Rewrite the expression.

$- - x - 2 (- \frac{5}{2}) = - 2 \cdot - 10$

Step 2.1.1.7

Multiply.

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Step 2.1.1.7.1

Multiply $- 1$ by $- 1$ .

$1 x - 2 (- \frac{5}{2}) = - 2 \cdot - 10$

Step 2.1.1.7.2

Multiply $x$ by $1$ .

$x - 2 (- \frac{5}{2}) = - 2 \cdot - 10$

Step 2.1.1.8

Cancel the common factor of $2$ .

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Step 2.1.1.8.1

Move the leading negative in $- \frac{5}{2}$ into the numerator.

$x - 2 (\frac{- 5}{2}) = - 2 \cdot - 10$

Step 2.1.1.8.2

Factor $2$ out of $- 2$ .

$x + 2 (- 1) \frac{- 5}{2} = - 2 \cdot - 10$

Step 2.1.1.8.3

Cancel the common factor.

$x + 2 \cdot - 1 \frac{- 5}{2} = - 2 \cdot - 10$

Step 2.1.1.8.4

Rewrite the expression.

$x - - 5 = - 2 \cdot - 10$

Step 2.1.1.9

Multiply $- 1$ by $- 5$ .

$x + 5 = - 2 \cdot - 10$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $- 2$ by $- 10$ .

$x + 5 = 20$

Step 3

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

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Step 3.1

Subtract $5$ from both sides of the equation.

$x = 20 - 5$

Step 3.2

Subtract $5$ from $20$ .

$x = 15$