Solve for y (3y+12)/4=2-(5y-7)/3

$\frac{3 y + 12}{4} = 2 - \frac{5 y - 7}{3}$

Step 1

Multiply both sides by $4$ .

$\frac{3 y + 12}{4} \cdot 4 = (2 - \frac{5 y - 7}{3}) \cdot 4$

Step 2

Simplify.

Simplify the left side.

Simplify $\frac{3 y + 12}{4} \cdot 4$ .

Factor $3$ out of $3 y + 12$ .

Factor $3$ out of $3 y$ .

$\frac{3 (y) + 12}{4} \cdot 4 = (2 - \frac{5 y - 7}{3}) \cdot 4$

Factor $3$ out of $12$ .

$\frac{3 y + 3 \cdot 4}{4} \cdot 4 = (2 - \frac{5 y - 7}{3}) \cdot 4$

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

$\frac{3 (y + 4)}{4} \cdot 4 = (2 - \frac{5 y - 7}{3}) \cdot 4$

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{3 (y + 4)}{4} \cdot 4 = (2 - \frac{5 y - 7}{3}) \cdot 4$

Rewrite the expression.

$3 (y + 4) = (2 - \frac{5 y - 7}{3}) \cdot 4$

Apply the distributive property.

$3 y + 3 \cdot 4 = (2 - \frac{5 y - 7}{3}) \cdot 4$

Multiply $3$ by $4$ .

$3 y + 12 = (2 - \frac{5 y - 7}{3}) \cdot 4$

Simplify the right side.

Simplify $(2 - \frac{5 y - 7}{3}) \cdot 4$ .

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

$3 y + 12 = (2 \cdot \frac{3}{3} - \frac{5 y - 7}{3}) \cdot 4$

Simplify terms.

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

$3 y + 12 = (\frac{2 \cdot 3}{3} - \frac{5 y - 7}{3}) \cdot 4$

Combine the numerators over the common denominator.

$3 y + 12 = \frac{2 \cdot 3 - (5 y - 7)}{3} \cdot 4$

Simplify the numerator.

Multiply $2$ by $3$ .

$3 y + 12 = \frac{6 - (5 y - 7)}{3} \cdot 4$

Apply the distributive property.

$3 y + 12 = \frac{6 - (5 y) - - 7}{3} \cdot 4$

Multiply $5$ by $- 1$ .

$3 y + 12 = \frac{6 - 5 y - - 7}{3} \cdot 4$

Multiply $- 1$ by $- 7$ .

$3 y + 12 = \frac{6 - 5 y + 7}{3} \cdot 4$

Add $6$ and $7$ .

$3 y + 12 = \frac{- 5 y + 13}{3} \cdot 4$

Simplify terms.

Combine $\frac{- 5 y + 13}{3}$ and $4$ .

$3 y + 12 = \frac{(- 5 y + 13) \cdot 4}{3}$

Move $4$ to the left of $- 5 y + 13$ .

$3 y + 12 = \frac{4 \cdot (- 5 y + 13)}{3}$

Factor $- 1$ out of $- 5 y$ .

$3 y + 12 = \frac{4 (- (5 y) + 13)}{3}$

Rewrite $13$ as $- 1 (- 13)$ .

$3 y + 12 = \frac{4 (- (5 y) - 1 (- 13))}{3}$

Factor $- 1$ out of $- (5 y) - 1 (- 13)$ .

$3 y + 12 = \frac{4 (- (5 y - 13))}{3}$

Simplify the expression.

Rewrite $- (5 y - 13)$ as $- 1 (5 y - 13)$ .

$3 y + 12 = \frac{4 (- 1 (5 y - 13))}{3}$

Move the negative in front of the fraction.

$3 y + 12 = - \frac{4 (5 y - 13)}{3}$

Step 3

Solve for $y$ .

Multiply both sides by $3$ .

$(3 y + 12) \cdot 3 = - \frac{4 (5 y - 13)}{3} \cdot 3$

Simplify.

Simplify the left side.

Simplify $(3 y + 12) \cdot 3$ .

Apply the distributive property.

$3 y \cdot 3 + 12 \cdot 3 = - \frac{4 (5 y - 13)}{3} \cdot 3$

Multiply.

Multiply $3$ by $3$ .

$9 y + 12 \cdot 3 = - \frac{4 (5 y - 13)}{3} \cdot 3$

Multiply $12$ by $3$ .

$9 y + 36 = - \frac{4 (5 y - 13)}{3} \cdot 3$

Simplify the right side.

Simplify $- \frac{4 (5 y - 13)}{3} \cdot 3$ .

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{4 (5 y - 13)}{3}$ into the numerator.

$9 y + 36 = \frac{- 4 (5 y - 13)}{3} \cdot 3$

Cancel the common factor.

$9 y + 36 = \frac{- 4 (5 y - 13)}{3} \cdot 3$

Rewrite the expression.

$9 y + 36 = - 4 (5 y - 13)$

Apply the distributive property.

$9 y + 36 = - 4 (5 y) - 4 \cdot - 13$

Multiply.

Multiply $5$ by $- 4$ .

$9 y + 36 = - 20 y - 4 \cdot - 13$

Multiply $- 4$ by $- 13$ .

$9 y + 36 = - 20 y + 52$

Solve for $y$ .

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

Add $20 y$ to both sides of the equation.

$9 y + 36 + 20 y = 52$

Add $9 y$ and $20 y$ .

$29 y + 36 = 52$

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

Subtract $36$ from both sides of the equation.

$29 y = 52 - 36$

Subtract $36$ from $52$ .

$29 y = 16$

Divide each term in $29 y = 16$ by $29$ and simplify.

Divide each term in $29 y = 16$ by $29$ .

$\frac{29 y}{29} = \frac{16}{29}$

Simplify the left side.

Cancel the common factor of $29$ .

Cancel the common factor.

$\frac{29 y}{29} = \frac{16}{29}$

Divide $y$ by $1$ .

$y = \frac{16}{29}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = \frac{16}{29}$

Decimal Form:

$y = 0.55172413 \dots$

Solve for y (3y+12)/4=2-(5y-7)/3

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