Solve for x (4|x+3|)/3=8

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

Step 1

Multiply both sides of the equation by $\frac{3}{4}$ .

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

Step 2

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{3}{4} \cdot \frac{4 | x + 3 |}{3}$ .

Cancel the common factor of $3$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{4} (4 | x + 3 |) = \frac{3}{4} \cdot 8$

Cancel the common factor of $4$ .

Factor $4$ out of $4 | x + 3 |$ .

$\frac{1}{4} (4 (| x + 3 |)) = \frac{3}{4} \cdot 8$

Cancel the common factor.

$\frac{1}{4} (4 | x + 3 |) = \frac{3}{4} \cdot 8$

Rewrite the expression.

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

Simplify the right side.

Simplify $\frac{3}{4} \cdot 8$ .

Cancel the common factor of $4$ .

Factor $4$ out of $8$ .

$| x + 3 | = \frac{3}{4} \cdot (4 (2))$

Cancel the common factor.

$| x + 3 | = \frac{3}{4} \cdot (4 \cdot 2)$

Rewrite the expression.

$| x + 3 | = 3 \cdot 2$

Multiply $3$ by $2$ .

$| x + 3 | = 6$

Step 3

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

$x + 3 = \pm 6$

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.

$x + 3 = 6$

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

Subtract $3$ from both sides of the equation.

$x = 6 - 3$

Subtract $3$ from $6$ .

$x = 3$

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

$x + 3 = - 6$

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

Subtract $3$ from both sides of the equation.

$x = - 6 - 3$

Subtract $3$ from $- 6$ .

$x = - 9$

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

$x = 3, - 9$

Solve for x (4|x+3|)/3=8

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