Solve for y 31=|5y+4|

$31 = | 5 y + 4 |$

Rewrite the equation as $| 5 y + 4 | = 31$ .

$| 5 y + 4 | = 31$

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

$5 y + 4 = \pm 31$

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.

$5 y + 4 = 31$

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

Subtract $4$ from both sides of the equation.

$5 y = 31 - 4$

Subtract $4$ from $31$ .

$5 y = 27$

Divide each term in $5 y = 27$ by $5$ and simplify.

Divide each term in $5 y = 27$ by $5$ .

$\frac{5 y}{5} = \frac{27}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} = \frac{27}{5}$

Divide $y$ by $1$ .

$y = \frac{27}{5}$

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

$5 y + 4 = - 31$

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

Subtract $4$ from both sides of the equation.

$5 y = - 31 - 4$

Subtract $4$ from $- 31$ .

$5 y = - 35$

Divide each term in $5 y = - 35$ by $5$ and simplify.

Divide each term in $5 y = - 35$ by $5$ .

$\frac{5 y}{5} = \frac{- 35}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} = \frac{- 35}{5}$

Divide $y$ by $1$ .

$y = \frac{- 35}{5}$

Simplify the right side.

Divide $- 35$ by $5$ .

$y = - 7$

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

$y = \frac{27}{5}, - 7$

The result can be shown in multiple forms.

Exact Form:

$y = \frac{27}{5}, - 7$

Decimal Form:

$y = 5.4, - 7$

Mixed Number Form:

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

Solve for y 31=|5y+4|

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