Solve for x |x+3|=2a+3

$| x + 3 | = 2 a + 3$

Step 1

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

$x + 3 = \pm (2 a + 3)$

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.

$x + 3 = 2 a + 3$

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

Subtract $3$ from both sides of the equation.

$x = 2 a + 3 - 3$

Combine the opposite terms in $2 a + 3 - 3$ .

Subtract $3$ from $3$ .

$x = 2 a + 0$

Add $2 a$ and $0$ .

$x = 2 a$

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

$x + 3 = - (2 a + 3)$

Simplify $- (2 a + 3)$ .

Rewrite.

$x + 3 = 0 + 0 - (2 a + 3)$

Simplify by adding zeros.

$x + 3 = - (2 a + 3)$

Apply the distributive property.

$x + 3 = - (2 a) - 1 \cdot 3$

Multiply.

Multiply $2$ by $- 1$ .

$x + 3 = - 2 a - 1 \cdot 3$

Multiply $- 1$ by $3$ .

$x + 3 = - 2 a - 3$

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

Subtract $3$ from both sides of the equation.

$x = - 2 a - 3 - 3$

Subtract $3$ from $- 3$ .

$x = - 2 a - 6$

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

$x = 2 a$

$x = - 2 a - 6$

$x = 2 a$

$x = - 2 a - 6$