Solve the Absolute Value Inequality for x 2-5|5x-5|=-73

$2 - 5 | 5 x - 5 | = - 73$

Step 1

Move all terms not containing $| 5 x - 5 |$ to the right side of the equation.

Subtract $2$ from both sides of the equation.

$- 5 | 5 x - 5 | = - 73 - 2$

Subtract $2$ from $- 73$ .

$- 5 | 5 x - 5 | = - 75$

Step 2

Divide each term in $- 5 | 5 x - 5 | = - 75$ by $- 5$ and simplify.

Divide each term in $- 5 | 5 x - 5 | = - 75$ by $- 5$ .

$\frac{- 5 | 5 x - 5 |}{- 5} = \frac{- 75}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 | 5 x - 5 |}{- 5} = \frac{- 75}{- 5}$

Divide $| 5 x - 5 |$ by $1$ .

$| 5 x - 5 | = \frac{- 75}{- 5}$

Simplify the right side.

Divide $- 75$ by $- 5$ .

$| 5 x - 5 | = 15$

Step 3

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

$5 x - 5 = \pm 15$

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.

$5 x - 5 = 15$

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

Add $5$ to both sides of the equation.

$5 x = 15 + 5$

Add $15$ and $5$ .

$5 x = 20$

Divide each term in $5 x = 20$ by $5$ and simplify.

Divide each term in $5 x = 20$ by $5$ .

$\frac{5 x}{5} = \frac{20}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{20}{5}$

Divide $x$ by $1$ .

$x = \frac{20}{5}$

Simplify the right side.

Divide $20$ by $5$ .

$x = 4$

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

$5 x - 5 = - 15$

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

Add $5$ to both sides of the equation.

$5 x = - 15 + 5$

Add $- 15$ and $5$ .

$5 x = - 10$

Divide each term in $5 x = - 10$ by $5$ and simplify.

Divide each term in $5 x = - 10$ by $5$ .

$\frac{5 x}{5} = \frac{- 10}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 10}{5}$

Divide $x$ by $1$ .

$x = \frac{- 10}{5}$

Simplify the right side.

Divide $- 10$ by $5$ .

$x = - 2$

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

$x = 4, - 2$

Solve the Absolute Value Inequality for x 2-5|5x-5|=-73

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