Solve for x |2x+3|+9=11

$| 2 x + 3 | + 9 = 11$

Step 1

Move all terms not containing $| 2 x + 3 |$ to the right side of the equation.

Subtract $9$ from both sides of the equation.

$| 2 x + 3 | = 11 - 9$

Subtract $9$ from $11$ .

$| 2 x + 3 | = 2$

Step 2

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

$2 x + 3 = \pm 2$

Step 3

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.

$2 x + 3 = 2$

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

Subtract $3$ from both sides of the equation.

$2 x = 2 - 3$

Subtract $3$ from $2$ .

$2 x = - 1$

Divide each term in $2 x = - 1$ by $2$ and simplify.

Divide each term in $2 x = - 1$ by $2$ .

$\frac{2 x}{2} = \frac{- 1}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 1}{2}$

Divide $x$ by $1$ .

$x = \frac{- 1}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{1}{2}$

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

$2 x + 3 = - 2$

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

Subtract $3$ from both sides of the equation.

$2 x = - 2 - 3$

Subtract $3$ from $- 2$ .

$2 x = - 5$

Divide each term in $2 x = - 5$ by $2$ and simplify.

Divide each term in $2 x = - 5$ by $2$ .

$\frac{2 x}{2} = \frac{- 5}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 5}{2}$

Divide $x$ by $1$ .

$x = \frac{- 5}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{5}{2}$

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

$x = - \frac{1}{2}, - \frac{5}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{1}{2}, - \frac{5}{2}$

Decimal Form:

$x = - 0.5, - 2.5$

Mixed Number Form:

$x = - \frac{1}{2}, - 2 \frac{1}{2}$

Solve for x |2x+3|+9=11

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