Solve the Absolute Value Inequality for x 6|1-5x|-9=57

$6 | 1 - 5 x | - 9 = 57$

Step 1

Move all terms not containing $| 1 - 5 x |$ to the right side of the equation.

Add $9$ to both sides of the equation.

$6 | 1 - 5 x | = 57 + 9$

Add $57$ and $9$ .

$6 | 1 - 5 x | = 66$

Step 2

Divide each term in $6 | 1 - 5 x | = 66$ by $6$ and simplify.

Divide each term in $6 | 1 - 5 x | = 66$ by $6$ .

$\frac{6 | 1 - 5 x |}{6} = \frac{66}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 | 1 - 5 x |}{6} = \frac{66}{6}$

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

$| 1 - 5 x | = \frac{66}{6}$

Simplify the right side.

Divide $66$ by $6$ .

$| 1 - 5 x | = 11$

Step 3

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

$1 - 5 x = \pm 11$

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.

$1 - 5 x = 11$

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

Subtract $1$ from both sides of the equation.

$- 5 x = 11 - 1$

Subtract $1$ from $11$ .

$- 5 x = 10$

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 $- 5$ .

$x = - 2$

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

$1 - 5 x = - 11$

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

Subtract $1$ from both sides of the equation.

$- 5 x = - 11 - 1$

Subtract $1$ from $- 11$ .

$- 5 x = - 12$

Divide each term in $- 5 x = - 12$ by $- 5$ and simplify.

Divide each term in $- 5 x = - 12$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{- 12}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{- 12}{- 5}$

Divide $x$ by $1$ .

$x = \frac{- 12}{- 5}$

Simplify the right side.

Dividing two negative values results in a positive value.

$x = \frac{12}{5}$

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

$x = - 2, \frac{12}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = - 2, \frac{12}{5}$

Decimal Form:

$x = - 2, 2.4$

Mixed Number Form:

$x = - 2, 2 \frac{2}{5}$

Solve the Absolute Value Inequality for x 6|1-5x|-9=57

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