Algebra Examples

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

Step 1

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

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

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

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Step 2.1.1.1

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

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

Step 2.1.1.2

Cancel the common factor of $5$ .

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Step 2.1.1.2.1

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

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

Step 2.1.1.2.2

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

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

Step 2.1.1.2.3

Factor $5$ out of $- 5$ .

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

Step 2.1.1.2.4

Cancel the common factor.

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

Step 2.1.1.2.5

Rewrite the expression.

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

Step 2.1.1.3

Cancel the common factor of $2$ .

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Step 2.1.1.3.1

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

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

Step 2.1.1.3.2

Cancel the common factor.

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

Step 2.1.1.3.3

Rewrite the expression.

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

Step 2.1.1.4

Multiply.

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Step 2.1.1.4.1

Multiply $- 1$ by $- 1$ .

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

Step 2.1.1.4.2

Multiply $x$ by $1$ .

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

Step 2.2

Simplify the right side.

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Step 2.2.1

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

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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 $- \frac{5}{2}$ into the numerator.

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

Step 2.2.1.1.2

Factor $5$ out of $- 5$ .

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

Step 2.2.1.1.3

Cancel the common factor.

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

Step 2.2.1.1.4

Rewrite the expression.

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

Step 2.2.1.2

Move the negative in front of the fraction.

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

Step 3

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$x = - 0.5$