Solve for x |7x-4|=8

$| 7 x - 4 | = 8$

Step 1

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

$7 x - 4 = \pm 8$

Step 2

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.

$7 x - 4 = 8$

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

Add $4$ to both sides of the equation.

$7 x = 8 + 4$

Add $8$ and $4$ .

$7 x = 12$

Divide each term in $7 x = 12$ by $7$ and simplify.

Divide each term in $7 x = 12$ by $7$ .

$\frac{7 x}{7} = \frac{12}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{12}{7}$

Divide $x$ by $1$ .

$x = \frac{12}{7}$

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

$7 x - 4 = - 8$

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

Add $4$ to both sides of the equation.

$7 x = - 8 + 4$

Add $- 8$ and $4$ .

$7 x = - 4$

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

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

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

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

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

$x = \frac{12}{7}, - \frac{4}{7}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$x = \frac{12}{7}, - \frac{4}{7}$

Decimal Form:

$x = 1.\overline{714285}, - 0.\overline{571428}$

Mixed Number Form:

$x = 1 \frac{5}{7}, - \frac{4}{7}$

Solve for x |7x-4|=8

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