Solve for x 3|-8x|+8=80

$3 | - 8 x | + 8 = 80$

Step 1

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

Subtract $8$ from both sides of the equation.

$3 | - 8 x | = 80 - 8$

Subtract $8$ from $80$ .

$3 | - 8 x | = 72$

Step 2

Divide each term in $3 | - 8 x | = 72$ by $3$ and simplify.

Divide each term in $3 | - 8 x | = 72$ by $3$ .

$\frac{3 | - 8 x |}{3} = \frac{72}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 | - 8 x |}{3} = \frac{72}{3}$

Divide $| - 8 x |$ by $1$ .

$| - 8 x | = \frac{72}{3}$

Simplify the right side.

Divide $72$ by $3$ .

$| - 8 x | = 24$

Step 3

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

$- 8 x = \pm 24$

Step 4

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.

$- 8 x = 24$

Divide each term in $- 8 x = 24$ by $- 8$ and simplify.

Divide each term in $- 8 x = 24$ by $- 8$ .

$\frac{- 8 x}{- 8} = \frac{24}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 x}{- 8} = \frac{24}{- 8}$

Divide $x$ by $1$ .

$x = \frac{24}{- 8}$

Simplify the right side.

Divide $24$ by $- 8$ .

$x = - 3$

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

$- 8 x = - 24$

Divide each term in $- 8 x = - 24$ by $- 8$ and simplify.

Divide each term in $- 8 x = - 24$ by $- 8$ .

$\frac{- 8 x}{- 8} = \frac{- 24}{- 8}$

Simplify the left side.

Cancel the common factor of $- 8$ .

Cancel the common factor.

$\frac{- 8 x}{- 8} = \frac{- 24}{- 8}$

Divide $x$ by $1$ .

$x = \frac{- 24}{- 8}$

Simplify the right side.

Divide $- 24$ by $- 8$ .

$x = 3$

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

$x = - 3, 3$

Solve for x 3|-8x|+8=80

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