Solve for y |(3y-7)/4|=2

$| \frac{3 y - 7}{4} | = 2$

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$\frac{3 y - 7}{4} = \pm 2$

Set up the positive portion of the $\pm$ solution.

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

Solve the first equation for $y$ .

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Multiply both sides of the equation by $4$ .

$3 y - 7 = 2 \cdot (4)$

Remove parentheses.

$3 y - 7 = 2 \cdot (4)$

Multiply $2$ by $4$ .

$3 y - 7 = 8$

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

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Add $7$ to both sides of the equation.

$3 y = 8 + 7$

Add $8$ and $7$ .

$3 y = 15$

Divide each term by $3$ and simplify.

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Divide each term in $3 y = 15$ by $3$ .

$\frac{3 y}{3} = \frac{15}{3}$

Cancel the common factor of $3$ .

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Cancel the common factor.

$\frac{3 y}{3} = \frac{15}{3}$

Divide $y$ by $1$ .

$y = \frac{15}{3}$

Divide $15$ by $3$ .

$y = 5$

Set up the negative portion of the $\pm$ solution.

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

Solve the second equation for $y$ .

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Multiply both sides of the equation by $4$ .

$3 y - 7 = - 2 \cdot 4$

Remove parentheses.

$3 y - 7 = - 2 \cdot 4$

Multiply $- 2$ by $4$ .

$3 y - 7 = - 8$

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

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Add $7$ to both sides of the equation.

$3 y = - 8 + 7$

Add $- 8$ and $7$ .

$3 y = - 1$

Divide each term by $3$ and simplify.

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Divide each term in $3 y = - 1$ by $3$ .

$\frac{3 y}{3} = \frac{- 1}{3}$

Cancel the common factor of $3$ .

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Cancel the common factor.

$\frac{3 y}{3} = \frac{- 1}{3}$

Divide $y$ by $1$ .

$y = \frac{- 1}{3}$

Move the negative in front of the fraction.

$y = - \frac{1}{3}$

The solution to the equation includes both the positive and negative portions of the solution.

$y = 5, - \frac{1}{3}$

The result can be shown in multiple forms.

Exact Form:

$y = 5, - \frac{1}{3}$

Decimal Form:

$y = 5, - 0.\overline{3}$

Solve for y |(3y-7)/4|=2

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