Solve for y |4-2y|+5=9

$| 4 - 2 y | + 5 = 9$

Step 1

Move all terms not containing $| 4 - 2 y |$ to the right side of the equation.

Subtract $5$ from both sides of the equation.

$| 4 - 2 y | = 9 - 5$

Subtract $5$ from $9$ .

$| 4 - 2 y | = 4$

Step 2

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

$4 - 2 y = \pm 4$

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.

$4 - 2 y = 4$

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

Subtract $4$ from both sides of the equation.

$- 2 y = 4 - 4$

Subtract $4$ from $4$ .

$- 2 y = 0$

Divide each term in $- 2 y = 0$ by $- 2$ and simplify.

Divide each term in $- 2 y = 0$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{0}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{0}{- 2}$

Divide $y$ by $1$ .

$y = \frac{0}{- 2}$

Simplify the right side.

Divide $0$ by $- 2$ .

$y = 0$

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

$4 - 2 y = - 4$

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

Subtract $4$ from both sides of the equation.

$- 2 y = - 4 - 4$

Subtract $4$ from $- 4$ .

$- 2 y = - 8$

Divide each term in $- 2 y = - 8$ by $- 2$ and simplify.

Divide each term in $- 2 y = - 8$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{- 8}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{- 8}{- 2}$

Divide $y$ by $1$ .

$y = \frac{- 8}{- 2}$

Simplify the right side.

Divide $- 8$ by $- 2$ .

$y = 4$

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

$y = 0, 4$

Solve for y |4-2y|+5=9

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