Basic Math Examples

$32 - \frac{3}{8} y = \frac{3}{4} y + 5$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Combine $y$ and $\frac{3}{8}$ .

$32 - \frac{y \cdot 3}{8} = \frac{3}{4} y + 5$

Step 1.2

Move $3$ to the left of $y$ .

$32 - \frac{3 y}{8} = \frac{3}{4} y + 5$

Step 2

Combine $\frac{3}{4}$ and $y$ .

$32 - \frac{3 y}{8} = \frac{3 y}{4} + 5$

Step 3

Move all terms containing $y$ to the left side of the equation.

Tap for more steps...

Step 3.1

Subtract $\frac{3 y}{4}$ from both sides of the equation.

$32 - \frac{3 y}{8} - \frac{3 y}{4} = 5$

Step 3.2

To write $- \frac{3 y}{4}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$32 - \frac{3 y}{8} - \frac{3 y}{4} \cdot \frac{2}{2} = 5$

Step 3.3

Write each expression with a common denominator of $8$ , by multiplying each by an appropriate factor of $1$ .

Tap for more steps...

Step 3.3.1

Multiply $\frac{3 y}{4}$ by $\frac{2}{2}$ .

$32 - \frac{3 y}{8} - \frac{3 y \cdot 2}{4 \cdot 2} = 5$

Step 3.3.2

Multiply $4$ by $2$ .

$32 - \frac{3 y}{8} - \frac{3 y \cdot 2}{8} = 5$

Step 3.4

Combine the numerators over the common denominator.

$32 + \frac{- 3 y - 3 y \cdot 2}{8} = 5$

Step 3.5

Simplify each term.

Tap for more steps...

Step 3.5.1

Simplify the numerator.

Tap for more steps...

Step 3.5.1.1

Factor $3 y$ out of $- 3 y - 3 y \cdot 2$ .

Tap for more steps...

Step 3.5.1.1.1

Factor $3 y$ out of $- 3 y$ .

$32 + \frac{3 y (- 1) - 3 y \cdot 2}{8} = 5$

Step 3.5.1.1.2

Factor $3 y$ out of $- 3 y \cdot 2$ .

$32 + \frac{3 y (- 1) + 3 y (- 1 \cdot 2)}{8} = 5$

Step 3.5.1.1.3

Factor $3 y$ out of $3 y (- 1) + 3 y (- 1 \cdot 2)$ .

$32 + \frac{3 y (- 1 - 1 \cdot 2)}{8} = 5$

Step 3.5.1.2

Multiply $- 1$ by $2$ .

$32 + \frac{3 y (- 1 - 2)}{8} = 5$

Step 3.5.1.3

Subtract $2$ from $- 1$ .

$32 + \frac{3 y \cdot - 3}{8} = 5$

Step 3.5.1.4

Multiply $- 3$ by $3$ .

$32 + \frac{- 9 y}{8} = 5$

Step 3.5.2

Move the negative in front of the fraction.

$32 - \frac{9 y}{8} = 5$

Step 4

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

Tap for more steps...

Step 4.1

Subtract $32$ from both sides of the equation.

$- \frac{9 y}{8} = 5 - 32$

Step 4.2

Subtract $32$ from $5$ .

$- \frac{9 y}{8} = - 27$

Step 5

Multiply both sides of the equation by $- \frac{8}{9}$ .

$- \frac{8}{9} (- \frac{9 y}{8}) = - \frac{8}{9} \cdot - 27$

Step 6

Simplify both sides of the equation.

Tap for more steps...

Step 6.1

Simplify the left side.

Tap for more steps...

Step 6.1.1

Simplify $- \frac{8}{9} (- \frac{9 y}{8})$ .

Tap for more steps...

Step 6.1.1.1

Cancel the common factor of $8$ .

Tap for more steps...

Step 6.1.1.1.1

Move the leading negative in $- \frac{8}{9}$ into the numerator.

$\frac{- 8}{9} (- \frac{9 y}{8}) = - \frac{8}{9} \cdot - 27$

Step 6.1.1.1.2

Move the leading negative in $- \frac{9 y}{8}$ into the numerator.

$\frac{- 8}{9} \cdot \frac{- 9 y}{8} = - \frac{8}{9} \cdot - 27$

Step 6.1.1.1.3

Factor $8$ out of $- 8$ .

$\frac{8 (- 1)}{9} \cdot \frac{- 9 y}{8} = - \frac{8}{9} \cdot - 27$

Step 6.1.1.1.4

Cancel the common factor.

$\frac{8 \cdot - 1}{9} \cdot \frac{- 9 y}{8} = - \frac{8}{9} \cdot - 27$

Step 6.1.1.1.5

Rewrite the expression.

$\frac{- 1}{9} (- 9 y) = - \frac{8}{9} \cdot - 27$

Step 6.1.1.2

Cancel the common factor of $9$ .

Tap for more steps...

Step 6.1.1.2.1

Factor $9$ out of $- 9 y$ .

$\frac{- 1}{9} (9 (- y)) = - \frac{8}{9} \cdot - 27$

Step 6.1.1.2.2

Cancel the common factor.

$\frac{- 1}{9} (9 (- y)) = - \frac{8}{9} \cdot - 27$

Step 6.1.1.2.3

Rewrite the expression.

$- - y = - \frac{8}{9} \cdot - 27$

Step 6.1.1.3

Multiply.

Tap for more steps...

Step 6.1.1.3.1

Multiply $- 1$ by $- 1$ .

$1 y = - \frac{8}{9} \cdot - 27$

Step 6.1.1.3.2

Multiply $y$ by $1$ .

$y = - \frac{8}{9} \cdot - 27$

Step 6.2

Simplify the right side.

Tap for more steps...

Step 6.2.1

Simplify $- \frac{8}{9} \cdot - 27$ .

Tap for more steps...

Step 6.2.1.1

Cancel the common factor of $9$ .

Tap for more steps...

Step 6.2.1.1.1

Move the leading negative in $- \frac{8}{9}$ into the numerator.

$y = \frac{- 8}{9} \cdot - 27$

Step 6.2.1.1.2

Factor $9$ out of $- 27$ .

$y = \frac{- 8}{9} \cdot (9 (- 3))$

Step 6.2.1.1.3

Cancel the common factor.

$y = \frac{- 8}{9} \cdot (9 \cdot - 3)$

Step 6.2.1.1.4

Rewrite the expression.

$y = - 8 \cdot - 3$

Step 6.2.1.2

Multiply $- 8$ by $- 3$ .

$y = 24$