Solve for y |-8y+6|=34

$| - 8 y + 6 | = 34$

Step 1

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

$- 8 y + 6 = \pm 34$

Step 2

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$- 8 y + 6 = 34$

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

Subtract $6$ from both sides of the equation.

$- 8 y = 34 - 6$

Subtract $6$ from $34$ .

$- 8 y = 28$

Divide each term in $- 8 y = 28$ by $- 8$ and simplify.

Divide each term in $- 8 y = 28$ by $- 8$ .

$\frac{- 8 y}{- 8} = \frac{28}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 y}{- 8} = \frac{28}{- 8}$

Divide $y$ by $1$ .

$y = \frac{28}{- 8}$

Simplify the right side.

Cancel the common factor of $28$ and $- 8$ .

Factor $4$ out of $28$ .

$y = \frac{4 (7)}{- 8}$

Cancel the common factors.

Factor $4$ out of $- 8$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Next, use the negative value of the $\pm$ to find the second solution.

$- 8 y + 6 = - 34$

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

Subtract $6$ from both sides of the equation.

$- 8 y = - 34 - 6$

Subtract $6$ from $- 34$ .

$- 8 y = - 40$

Divide each term in $- 8 y = - 40$ by $- 8$ and simplify.

Divide each term in $- 8 y = - 40$ by $- 8$ .

$\frac{- 8 y}{- 8} = \frac{- 40}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 y}{- 8} = \frac{- 40}{- 8}$

Divide $y$ by $1$ .

$y = \frac{- 40}{- 8}$

Simplify the right side.

Divide $- 40$ by $- 8$ .

$y = 5$

The complete solution is the result of both the positive and negative portions of the solution.

$y = - \frac{7}{2}, 5$

Step 3

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{7}{2}, 5$

Decimal Form:

$y = - 3.5, 5$

Mixed Number Form:

$y = - 3 \frac{1}{2}, 5$

Solve for y |-8y+6|=34

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