Solve for y 41=|13-4y|

$41 = | 13 - 4 y |$

Step 1

Rewrite the equation as $| 13 - 4 y | = 41$ .

$| 13 - 4 y | = 41$

Step 2

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

$13 - 4 y = \pm 41$

Step 3

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.

$13 - 4 y = 41$

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

Subtract $13$ from both sides of the equation.

$- 4 y = 41 - 13$

Subtract $13$ from $41$ .

$- 4 y = 28$

Divide each term in $- 4 y = 28$ by $- 4$ and simplify.

Divide each term in $- 4 y = 28$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{28}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{28}{- 4}$

Divide $y$ by $1$ .

$y = \frac{28}{- 4}$

Simplify the right side.

Divide $28$ by $- 4$ .

$y = - 7$

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

$13 - 4 y = - 41$

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

Subtract $13$ from both sides of the equation.

$- 4 y = - 41 - 13$

Subtract $13$ from $- 41$ .

$- 4 y = - 54$

Divide each term in $- 4 y = - 54$ by $- 4$ and simplify.

Divide each term in $- 4 y = - 54$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{- 54}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{- 54}{- 4}$

Divide $y$ by $1$ .

$y = \frac{- 54}{- 4}$

Simplify the right side.

Cancel the common factor of $- 54$ and $- 4$ .

Factor $- 2$ out of $- 54$ .

$y = \frac{- 2 (27)}{- 4}$

Cancel the common factors.

Factor $- 2$ out of $- 4$ .

$y = \frac{- 2 \cdot 27}{- 2 \cdot 2}$

Cancel the common factor.

$y = \frac{- 2 \cdot 27}{- 2 \cdot 2}$

Rewrite the expression.

$y = \frac{27}{2}$

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

$y = - 7, \frac{27}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$y = - 7, \frac{27}{2}$

Decimal Form:

$y = - 7, 13.5$

Mixed Number Form:

$y = - 7, 13 \frac{1}{2}$

Solve for y 41=|13-4y|

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