Solve for x -4+|8-8x|=52

$- 4 + | 8 - 8 x | = 52$

Step 1

Move all terms not containing $| 8 - 8 x |$ to the right side of the equation.

Add $4$ to both sides of the equation.

$| 8 - 8 x | = 52 + 4$

Add $52$ and $4$ .

$| 8 - 8 x | = 56$

Step 2

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

$8 - 8 x = \pm 56$

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.

$8 - 8 x = 56$

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

Subtract $8$ from both sides of the equation.

$- 8 x = 56 - 8$

Subtract $8$ from $56$ .

$- 8 x = 48$

Divide each term in $- 8 x = 48$ by $- 8$ and simplify.

Divide each term in $- 8 x = 48$ by $- 8$ .

$\frac{- 8 x}{- 8} = \frac{48}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 x}{- 8} = \frac{48}{- 8}$

Divide $x$ by $1$ .

$x = \frac{48}{- 8}$

Simplify the right side.

Divide $48$ by $- 8$ .

$x = - 6$

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

$8 - 8 x = - 56$

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

Subtract $8$ from both sides of the equation.

$- 8 x = - 56 - 8$

Subtract $8$ from $- 56$ .

$- 8 x = - 64$

Divide each term in $- 8 x = - 64$ by $- 8$ and simplify.

Divide each term in $- 8 x = - 64$ by $- 8$ .

$\frac{- 8 x}{- 8} = \frac{- 64}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 x}{- 8} = \frac{- 64}{- 8}$

Divide $x$ by $1$ .

$x = \frac{- 64}{- 8}$

Simplify the right side.

Divide $- 64$ by $- 8$ .

$x = 8$

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

$x = - 6, 8$

Solve for x -4+|8-8x|=52

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