Basic Math Examples

$\frac{2}{5} b + \frac{4}{5} = - \frac{6}{5}$

Step 1

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

$\frac{2 b}{5} + \frac{4}{5} = - \frac{6}{5}$

Step 2

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

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Step 2.1

Subtract $\frac{4}{5}$ from both sides of the equation.

$\frac{2 b}{5} = - \frac{6}{5} - \frac{4}{5}$

Step 2.2

Combine the numerators over the common denominator.

$\frac{2 b}{5} = \frac{- 6 - 4}{5}$

Step 2.3

Subtract $4$ from $- 6$ .

$\frac{2 b}{5} = \frac{- 10}{5}$

Step 2.4

Divide $- 10$ by $5$ .

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

Step 3

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

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

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 $\frac{5}{2} \cdot \frac{2 b}{5}$ .

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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

Cancel the common factor.

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

Step 4.1.1.1.2

Rewrite the expression.

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

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 $2 b$ .

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

Step 4.1.1.2.2

Cancel the common factor.

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

Step 4.1.1.2.3

Rewrite the expression.

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

Step 4.2

Simplify the right side.

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Step 4.2.1

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

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Step 4.2.1.1

Cancel the common factor of $2$ .

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Step 4.2.1.1.1

Factor $2$ out of $- 2$ .

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

Step 4.2.1.1.2

Cancel the common factor.

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

Step 4.2.1.1.3

Rewrite the expression.

$b = 5 \cdot - 1$

Step 4.2.1.2

Multiply $5$ by $- 1$ .

$b = - 5$