Solve for x 8|5x-2|=40

$8 | 5 x - 2 | = 40$

Step 1

Divide each term in $8 | 5 x - 2 | = 40$ by $8$ and simplify.

Divide each term in $8 | 5 x - 2 | = 40$ by $8$ .

$\frac{8 | 5 x - 2 |}{8} = \frac{40}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 | 5 x - 2 |}{8} = \frac{40}{8}$

Divide $| 5 x - 2 |$ by $1$ .

$| 5 x - 2 | = \frac{40}{8}$

Simplify the right side.

Divide $40$ by $8$ .

$| 5 x - 2 | = 5$

Step 2

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

$5 x - 2 = \pm 5$

Step 3

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.

$5 x - 2 = 5$

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

Add $2$ to both sides of the equation.

$5 x = 5 + 2$

Add $5$ and $2$ .

$5 x = 7$

Divide each term in $5 x = 7$ by $5$ and simplify.

Divide each term in $5 x = 7$ by $5$ .

$\frac{5 x}{5} = \frac{7}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{7}{5}$

Divide $x$ by $1$ .

$x = \frac{7}{5}$

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

$5 x - 2 = - 5$

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

Add $2$ to both sides of the equation.

$5 x = - 5 + 2$

Add $- 5$ and $2$ .

$5 x = - 3$

Divide each term in $5 x = - 3$ by $5$ and simplify.

Divide each term in $5 x = - 3$ by $5$ .

$\frac{5 x}{5} = \frac{- 3}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{- 3}{5}$

Divide $x$ by $1$ .

$x = \frac{- 3}{5}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{3}{5}$

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

$x = \frac{7}{5}, - \frac{3}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{7}{5}, - \frac{3}{5}$

Decimal Form:

$x = 1.4, - 0.6$

Mixed Number Form:

$x = 1 \frac{2}{5}, - \frac{3}{5}$

Solve for x 8|5x-2|=40

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