Solve the Absolute Value Inequality for x (2|x+1|)/3=6

$\frac{2 | x + 1 |}{3} = 6$

Step 1

Multiply both sides of the equation by $\frac{3}{2}$ .

$\frac{3}{2} \cdot \frac{2 | x + 1 |}{3} = \frac{3}{2} \cdot 6$

Step 2

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{3}{2} \cdot \frac{2 | x + 1 |}{3}$ .

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3}{2} \cdot \frac{2 | x + 1 |}{3} = \frac{3}{2} \cdot 6$

Rewrite the expression.

$\frac{1}{2} (2 | x + 1 |) = \frac{3}{2} \cdot 6$

Cancel the common factor of $2$ .

Factor $2$ out of $2 | x + 1 |$ .

$\frac{1}{2} (2 (| x + 1 |)) = \frac{3}{2} \cdot 6$

Cancel the common factor.

$\frac{1}{2} (2 | x + 1 |) = \frac{3}{2} \cdot 6$

Rewrite the expression.

$| x + 1 | = \frac{3}{2} \cdot 6$

Simplify the right side.

Simplify $\frac{3}{2} \cdot 6$ .

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$| x + 1 | = \frac{3}{2} \cdot (2 (3))$

Cancel the common factor.

$| x + 1 | = \frac{3}{2} \cdot (2 \cdot 3)$

Rewrite the expression.

$| x + 1 | = 3 \cdot 3$

Multiply $3$ by $3$ .

$| x + 1 | = 9$

Step 3

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

$x + 1 = \pm 9$

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.

$x + 1 = 9$

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

Subtract $1$ from both sides of the equation.

$x = 9 - 1$

Subtract $1$ from $9$ .

$x = 8$

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

$x + 1 = - 9$

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

Subtract $1$ from both sides of the equation.

$x = - 9 - 1$

Subtract $1$ from $- 9$ .

$x = - 10$

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

$x = 8, - 10$

Solve the Absolute Value Inequality for x (2|x+1|)/3=6

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