Algebra Examples

$5 - \frac{2}{5} x = 8$

Step 1

Simplify each term.

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Step 1.1

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

$5 - \frac{x \cdot 2}{5} = 8$

Step 1.2

Move $2$ to the left of $x$ .

$5 - \frac{2 x}{5} = 8$

Step 2

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

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Step 2.1

Subtract $5$ from both sides of the equation.

$- \frac{2 x}{5} = 8 - 5$

Step 2.2

Subtract $5$ from $8$ .

$- \frac{2 x}{5} = 3$

Step 3

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

$- \frac{5}{2} (- \frac{2 x}{5}) = - \frac{5}{2} \cdot 3$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

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

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Step 4.1.1.1

Cancel the common factor of $5$ .

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Step 4.1.1.1.1

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

$\frac{- 5}{2} (- \frac{2 x}{5}) = - \frac{5}{2} \cdot 3$

Step 4.1.1.1.2

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

$\frac{- 5}{2} \cdot \frac{- 2 x}{5} = - \frac{5}{2} \cdot 3$

Step 4.1.1.1.3

Factor $5$ out of $- 5$ .

$\frac{5 (- 1)}{2} \cdot \frac{- 2 x}{5} = - \frac{5}{2} \cdot 3$

Step 4.1.1.1.4

Cancel the common factor.

$\frac{5 \cdot - 1}{2} \cdot \frac{- 2 x}{5} = - \frac{5}{2} \cdot 3$

Step 4.1.1.1.5

Rewrite the expression.

$\frac{- 1}{2} (- 2 x) = - \frac{5}{2} \cdot 3$

Step 4.1.1.2

Cancel the common factor of $2$ .

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Step 4.1.1.2.1

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

$\frac{- 1}{2} (2 (- x)) = - \frac{5}{2} \cdot 3$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{- 1}{2} (2 (- x)) = - \frac{5}{2} \cdot 3$

Step 4.1.1.2.3

Rewrite the expression.

$- - x = - \frac{5}{2} \cdot 3$

Step 4.1.1.3

Multiply.

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Step 4.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 x = - \frac{5}{2} \cdot 3$

Step 4.1.1.3.2

Multiply $x$ by $1$ .

$x = - \frac{5}{2} \cdot 3$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $- \frac{5}{2} \cdot 3$ .

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Step 4.2.1.1

Multiply $- \frac{5}{2} \cdot 3$ .

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Step 4.2.1.1.1

Multiply $3$ by $- 1$ .

$x = - 3 (\frac{5}{2})$

Step 4.2.1.1.2

Combine $- 3$ and $\frac{5}{2}$ .

$x = \frac{- 3 \cdot 5}{2}$

Step 4.2.1.1.3

Multiply $- 3$ by $5$ .

$x = \frac{- 15}{2}$

Step 4.2.1.2

Move the negative in front of the fraction.

$x = - \frac{15}{2}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{15}{2}$

Decimal Form:

$x = - 7.5$

Mixed Number Form:

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