Pre-Algebra Examples

$- \frac{5}{2} x = - 5$

Step 1

Multiply both sides of the equation by $- \frac{2}{5}$ .

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

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

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Step 2.1.1.1

Combine $x$ and $\frac{5}{2}$ .

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

Step 2.1.1.2

Cancel the common factor of $2$ .

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Step 2.1.1.2.1

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

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

Step 2.1.1.2.2

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

$\frac{- 2}{5} \cdot \frac{- x \cdot 5}{2} = - \frac{2}{5} \cdot - 5$

Step 2.1.1.2.3

Factor $2$ out of $- 2$ .

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

Step 2.1.1.2.4

Cancel the common factor.

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

Step 2.1.1.2.5

Rewrite the expression.

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

Step 2.1.1.3

Cancel the common factor of $5$ .

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Step 2.1.1.3.1

Factor $5$ out of $- x \cdot 5$ .

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

Step 2.1.1.3.2

Cancel the common factor.

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

Step 2.1.1.3.3

Rewrite the expression.

$- - x = - \frac{2}{5} \cdot - 5$

Step 2.1.1.4

Multiply.

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Step 2.1.1.4.1

Multiply $- 1$ by $- 1$ .

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

Step 2.1.1.4.2

Multiply $x$ by $1$ .

$x = - \frac{2}{5} \cdot - 5$

Step 2.2

Simplify the right side.

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Step 2.2.1

Simplify $- \frac{2}{5} \cdot - 5$ .

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Step 2.2.1.1

Cancel the common factor of $5$ .

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Step 2.2.1.1.1

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

$x = \frac{- 2}{5} \cdot - 5$

Step 2.2.1.1.2

Factor $5$ out of $- 5$ .

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

Step 2.2.1.1.3

Cancel the common factor.

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

Step 2.2.1.1.4

Rewrite the expression.

$x = - 2 \cdot - 1$

Step 2.2.1.2

Multiply $- 2$ by $- 1$ .

$x = 2$