Solve the Absolute Value Inequality for x (|7x+4|)/8=3

$\frac{| 7 x + 4 |}{8} = 3$

Multiply both sides by $8$ .

$\frac{| 7 x + 4 |}{8} \cdot 8 = 3 \cdot 8$

Simplify.

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{| 7 x + 4 |}{8} \cdot 8 = 3 \cdot 8$

Rewrite the expression.

$| 7 x + 4 | = 3 \cdot 8$

Simplify the right side.

Multiply $3$ by $8$ .

$| 7 x + 4 | = 24$

Solve for $x$ .

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

$7 x + 4 = \pm 24$

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.

$7 x + 4 = 24$

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

Subtract $4$ from both sides of the equation.

$7 x = 24 - 4$

Subtract $4$ from $24$ .

$7 x = 20$

Divide each term in $7 x = 20$ by $7$ and simplify.

Divide each term in $7 x = 20$ by $7$ .

$\frac{7 x}{7} = \frac{20}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{20}{7}$

Divide $x$ by $1$ .

$x = \frac{20}{7}$

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

$7 x + 4 = - 24$

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

Subtract $4$ from both sides of the equation.

$7 x = - 24 - 4$

Subtract $4$ from $- 24$ .

$7 x = - 28$

Divide each term in $7 x = - 28$ by $7$ and simplify.

Divide each term in $7 x = - 28$ by $7$ .

$\frac{7 x}{7} = \frac{- 28}{7}$

Simplify the left side.

Cancel the common factor of $7$ .

Cancel the common factor.

$\frac{7 x}{7} = \frac{- 28}{7}$

Divide $x$ by $1$ .

$x = \frac{- 28}{7}$

Simplify the right side.

Divide $- 28$ by $7$ .

$x = - 4$

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

$x = \frac{20}{7}, - 4$

The result can be shown in multiple forms.

Exact Form:

$x = \frac{20}{7}, - 4$

Decimal Form:

$x = 2.\overline{857142}, - 4$

Mixed Number Form:

$x = 2 \frac{6}{7}, - 4$

Solve the Absolute Value Inequality for x (|7x+4|)/8=3

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