Algebra Examples

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

Step 1

Combine $b$ and $\frac{1}{5}$ .

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

Step 2

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

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Step 2.1

Add $\frac{2}{5}$ to both sides of the equation.

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

Step 2.2

To write $- 2$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

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

Step 2.3

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

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

Step 2.4

Combine the numerators over the common denominator.

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

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $- 2$ by $5$ .

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

Step 2.5.2

Add $- 10$ and $2$ .

$- \frac{b}{5} = \frac{- 8}{5}$

Step 2.6

Move the negative in front of the fraction.

$- \frac{b}{5} = - \frac{8}{5}$

Step 3

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- b = - 8$

Step 4

Divide each term in $- b = - 8$ by $- 1$ and simplify.

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Step 4.1

Divide each term in $- b = - 8$ by $- 1$ .

$\frac{- b}{- 1} = \frac{- 8}{- 1}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Dividing two negative values results in a positive value.

$\frac{b}{1} = \frac{- 8}{- 1}$

Step 4.2.2

Divide $b$ by $1$ .

$b = \frac{- 8}{- 1}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 8$ by $- 1$ .

$b = 8$