Solve for y 4/3y+2=4y-4

$\frac{4}{3} y + 2 = 4 y - 4$

Step 1

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

$\frac{4 y}{3} + 2 = 4 y - 4$

Step 2

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

Subtract $4 y$ from both sides of the equation.

$\frac{4 y}{3} + 2 - 4 y = - 4$

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

$\frac{4 y}{3} - 4 y \cdot \frac{3}{3} + 2 = - 4$

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

$\frac{4 y}{3} + \frac{- 4 y \cdot 3}{3} + 2 = - 4$

Combine the numerators over the common denominator.

$\frac{4 y - 4 y \cdot 3}{3} + 2 = - 4$

Simplify each term.

Simplify the numerator.

Factor $4 y$ out of $4 y - 4 y \cdot 3$ .

Factor $4 y$ out of $4 y$ .

$\frac{4 y (1) - 4 y \cdot 3}{3} + 2 = - 4$

Factor $4 y$ out of $- 4 y \cdot 3$ .

$\frac{4 y (1) + 4 y (- 1 \cdot 3)}{3} + 2 = - 4$

Factor $4 y$ out of $4 y (1) + 4 y (- 1 \cdot 3)$ .

$\frac{4 y (1 - 1 \cdot 3)}{3} + 2 = - 4$

Multiply $- 1$ by $3$ .

$\frac{4 y (1 - 3)}{3} + 2 = - 4$

Subtract $3$ from $1$ .

$\frac{4 y \cdot - 2}{3} + 2 = - 4$

Multiply $- 2$ by $4$ .

$\frac{- 8 y}{3} + 2 = - 4$

Move the negative in front of the fraction.

$- \frac{8 y}{3} + 2 = - 4$

Step 3

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

Subtract $2$ from both sides of the equation.

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

Subtract $2$ from $- 4$ .

$- \frac{8 y}{3} = - 6$

Step 4

Multiply both sides of the equation by $- \frac{3}{8}$ .

$- \frac{3}{8} (- \frac{8 y}{3}) = - \frac{3}{8} \cdot - 6$

Step 5

Simplify both sides of the equation.

Simplify the left side.

Simplify $- \frac{3}{8} (- \frac{8 y}{3})$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{3}{8}$ into the numerator.

$\frac{- 3}{8} (- \frac{8 y}{3}) = - \frac{3}{8} \cdot - 6$

Move the leading negative in $- \frac{8 y}{3}$ into the numerator.

$\frac{- 3}{8} \cdot \frac{- 8 y}{3} = - \frac{3}{8} \cdot - 6$

Factor $3$ out of $- 3$ .

$\frac{3 (- 1)}{8} \cdot \frac{- 8 y}{3} = - \frac{3}{8} \cdot - 6$

Cancel the common factor.

$\frac{3 \cdot - 1}{8} \cdot \frac{- 8 y}{3} = - \frac{3}{8} \cdot - 6$

Rewrite the expression.

$\frac{- 1}{8} (- 8 y) = - \frac{3}{8} \cdot - 6$

Cancel the common factor of $8$ .

Factor $8$ out of $- 8 y$ .

$\frac{- 1}{8} (8 (- y)) = - \frac{3}{8} \cdot - 6$

Cancel the common factor.

$\frac{- 1}{8} (8 (- y)) = - \frac{3}{8} \cdot - 6$

Rewrite the expression.

$- - y = - \frac{3}{8} \cdot - 6$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 y = - \frac{3}{8} \cdot - 6$

Multiply $y$ by $1$ .

$y = - \frac{3}{8} \cdot - 6$

Simplify the right side.

Simplify $- \frac{3}{8} \cdot - 6$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{3}{8}$ into the numerator.

$y = \frac{- 3}{8} \cdot - 6$

Factor $2$ out of $8$ .

$y = \frac{- 3}{2 (4)} \cdot - 6$

Factor $2$ out of $- 6$ .

$y = \frac{- 3}{2 \cdot 4} \cdot (2 \cdot - 3)$

Cancel the common factor.

$y = \frac{- 3}{2 \cdot 4} \cdot (2 \cdot - 3)$

Rewrite the expression.

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

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

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

Multiply $- 3$ by $- 3$ .

$y = \frac{9}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$y = \frac{9}{4}$

Decimal Form:

$y = 2.25$

Mixed Number Form:

$y = 2 \frac{1}{4}$

Solve for y 4/3y+2=4y-4

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