Solve the Absolute Value Inequality for x -4|x-7|+5=-19

$- 4 | x - 7 | + 5 = - 19$

Move all terms not containing $| x - 7 |$ to the right side of the equation.

Subtract $5$ from both sides of the equation.

$- 4 | x - 7 | = - 19 - 5$

Subtract $5$ from $- 19$ .

$- 4 | x - 7 | = - 24$

Divide each term in $- 4 | x - 7 | = - 24$ by $- 4$ and simplify.

Divide each term in $- 4 | x - 7 | = - 24$ by $- 4$ .

$\frac{- 4 | x - 7 |}{- 4} = \frac{- 24}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 | x - 7 |}{- 4} = \frac{- 24}{- 4}$

Divide $| x - 7 |$ by $1$ .

$| x - 7 | = \frac{- 24}{- 4}$

Simplify the right side.

Divide $- 24$ by $- 4$ .

$| x - 7 | = 6$

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

$x - 7 = \pm 6$

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.

$x - 7 = 6$

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

Add $7$ to both sides of the equation.

$x = 6 + 7$

Add $6$ and $7$ .

$x = 13$

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

$x - 7 = - 6$

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

Add $7$ to both sides of the equation.

$x = - 6 + 7$

Add $- 6$ and $7$ .

$x = 1$

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

$x = 13, 1$