Pre-Algebra Examples

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

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

Combine $y$ and $\frac{5}{3}$ .

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

Step 1.2

Move $5$ to the left of $y$ .

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

Step 2

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

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

Step 3

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

Tap for more steps...

Step 3.1

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

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

Step 3.2

Combine the numerators over the common denominator.

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

Step 3.3

Subtract $4 y$ from $- 5 y$ .

$\frac{- 9 y}{3} + \frac{- 5}{4} = - 3$

Step 3.4

Simplify each term.

Tap for more steps...

Step 3.4.1

Cancel the common factor of $- 9$ and $3$ .

Tap for more steps...

Step 3.4.1.1

Factor $3$ out of $- 9 y$ .

$\frac{3 (- 3 y)}{3} + \frac{- 5}{4} = - 3$

Step 3.4.1.2

Cancel the common factors.

Tap for more steps...

Step 3.4.1.2.1

Factor $3$ out of $3$ .

$\frac{3 (- 3 y)}{3 (1)} + \frac{- 5}{4} = - 3$

Step 3.4.1.2.2

Cancel the common factor.

$\frac{3 (- 3 y)}{3 \cdot 1} + \frac{- 5}{4} = - 3$

Step 3.4.1.2.3

Rewrite the expression.

$\frac{- 3 y}{1} + \frac{- 5}{4} = - 3$

Step 3.4.1.2.4

Divide $- 3 y$ by $1$ .

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

Step 3.4.2

Move the negative in front of the fraction.

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

Step 4

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

Tap for more steps...

Step 4.1

Add $\frac{5}{4}$ to both sides of the equation.

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

Step 4.2

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

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

Step 4.3

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

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

Step 4.4

Combine the numerators over the common denominator.

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

Step 4.5

Simplify the numerator.

Tap for more steps...

Step 4.5.1

Multiply $- 3$ by $4$ .

$- 3 y = \frac{- 12 + 5}{4}$

Step 4.5.2

Add $- 12$ and $5$ .

$- 3 y = \frac{- 7}{4}$

Step 4.6

Move the negative in front of the fraction.

$- 3 y = - \frac{7}{4}$

Step 5

Divide each term in $- 3 y = - \frac{7}{4}$ by $- 3$ and simplify.

Tap for more steps...

Step 5.1

Divide each term in $- 3 y = - \frac{7}{4}$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{- \frac{7}{4}}{- 3}$

Step 5.2

Simplify the left side.

Tap for more steps...

Step 5.2.1

Cancel the common factor of $- 3$ .

Tap for more steps...

Step 5.2.1.1

Cancel the common factor.

$\frac{- 3 y}{- 3} = \frac{- \frac{7}{4}}{- 3}$

Step 5.2.1.2

Divide $y$ by $1$ .

$y = \frac{- \frac{7}{4}}{- 3}$

Step 5.3

Simplify the right side.

Tap for more steps...

Step 5.3.1

Multiply the numerator by the reciprocal of the denominator.

$y = - \frac{7}{4} \cdot \frac{1}{- 3}$

Step 5.3.2

Move the negative in front of the fraction.

$y = - \frac{7}{4} (- \frac{1}{3})$

Step 5.3.3

Multiply $- \frac{7}{4} (- \frac{1}{3})$ .

Tap for more steps...

Step 5.3.3.1

Multiply $- 1$ by $- 1$ .

$y = 1 (\frac{7}{4}) \frac{1}{3}$

Step 5.3.3.2

Multiply $\frac{7}{4}$ by $1$ .

$y = \frac{7}{4} \cdot \frac{1}{3}$

Step 5.3.3.3

Multiply $\frac{7}{4}$ by $\frac{1}{3}$ .

$y = \frac{7}{4 \cdot 3}$

Step 5.3.3.4

Multiply $4$ by $3$ .

$y = \frac{7}{12}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$y = \frac{7}{12}$

Decimal Form:

$y = 0.58\overline{3}$