Solve the Absolute Value Inequality for x 2-2|7+2x|=0

$2 - 2 | 7 + 2 x | = 0$

Subtract $2$ from both sides of the equation.

$- 2 | 7 + 2 x | = - 2$

Divide each term in $- 2 | 7 + 2 x | = - 2$ by $- 2$ and simplify.

Divide each term in $- 2 | 7 + 2 x | = - 2$ by $- 2$ .

$\frac{- 2 | 7 + 2 x |}{- 2} = \frac{- 2}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 | 7 + 2 x |}{- 2} = \frac{- 2}{- 2}$

Divide $| 7 + 2 x |$ by $1$ .

$| 7 + 2 x | = \frac{- 2}{- 2}$

Simplify the right side.

Divide $- 2$ by $- 2$ .

$| 7 + 2 x | = 1$

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

$7 + 2 x = \pm 1$

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.

$7 + 2 x = 1$

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

Subtract $7$ from both sides of the equation.

$2 x = 1 - 7$

Subtract $7$ from $1$ .

$2 x = - 6$

Divide each term in $2 x = - 6$ by $2$ and simplify.

Divide each term in $2 x = - 6$ by $2$ .

$\frac{2 x}{2} = \frac{- 6}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 6}{2}$

Divide $x$ by $1$ .

$x = \frac{- 6}{2}$

Simplify the right side.

Divide $- 6$ by $2$ .

$x = - 3$

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

$7 + 2 x = - 1$

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

Subtract $7$ from both sides of the equation.

$2 x = - 1 - 7$

Subtract $7$ from $- 1$ .

$2 x = - 8$

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

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

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

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $- 8$ by $2$ .

$x = - 4$

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

$x = - 3, - 4$

Solve the Absolute Value Inequality for x 2-2|7+2x|=0

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