Pre-Algebra Examples

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

Step 1

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

Tap for more steps...

Step 1.1

Subtract $2$ from both sides of the equation.

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

Step 1.2

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

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

Step 1.3

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

$- \frac{b}{3} = - \frac{5}{2} + \frac{- 2 \cdot 2}{2}$

Step 1.4

Combine the numerators over the common denominator.

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

Step 1.5

Simplify the numerator.

Tap for more steps...

Step 1.5.1

Multiply $- 2$ by $2$ .

$- \frac{b}{3} = \frac{- 5 - 4}{2}$

Step 1.5.2

Subtract $4$ from $- 5$ .

$- \frac{b}{3} = \frac{- 9}{2}$

Step 1.6

Move the negative in front of the fraction.

$- \frac{b}{3} = - \frac{9}{2}$

Step 2

Multiply both sides of the equation by $- 3$ .

$- 3 (- \frac{b}{3}) = - 3 (- \frac{9}{2})$

Step 3

Simplify both sides of the equation.

Tap for more steps...

Step 3.1

Simplify the left side.

Tap for more steps...

Step 3.1.1

Simplify $- 3 (- \frac{b}{3})$ .

Tap for more steps...

Step 3.1.1.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 3.1.1.1.1

Move the leading negative in $- \frac{b}{3}$ into the numerator.

$- 3 \frac{- b}{3} = - 3 (- \frac{9}{2})$

Step 3.1.1.1.2

Factor $3$ out of $- 3$ .

$3 (- 1) \frac{- b}{3} = - 3 (- \frac{9}{2})$

Step 3.1.1.1.3

Cancel the common factor.

$3 \cdot - 1 \frac{- b}{3} = - 3 (- \frac{9}{2})$

Step 3.1.1.1.4

Rewrite the expression.

$- - b = - 3 (- \frac{9}{2})$

Step 3.1.1.2

Multiply.

Tap for more steps...

Step 3.1.1.2.1

Multiply $- 1$ by $- 1$ .

$1 b = - 3 (- \frac{9}{2})$

Step 3.1.1.2.2

Multiply $b$ by $1$ .

$b = - 3 (- \frac{9}{2})$

Step 3.2

Simplify the right side.

Tap for more steps...

Step 3.2.1

Multiply $- 3 (- \frac{9}{2})$ .

Tap for more steps...

Step 3.2.1.1

Multiply $- 1$ by $- 3$ .

$b = 3 (\frac{9}{2})$

Step 3.2.1.2

Combine $3$ and $\frac{9}{2}$ .

$b = \frac{3 \cdot 9}{2}$

Step 3.2.1.3

Multiply $3$ by $9$ .

$b = \frac{27}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$b = \frac{27}{2}$

Decimal Form:

$b = 13.5$

Mixed Number Form:

$b = 13 \frac{1}{2}$