Solve the Absolute Value Inequality for b 4=|2b+11|

$4 = | 2 b + 11 |$

Step 1

Rewrite the equation as $| 2 b + 11 | = 4$ .

$| 2 b + 11 | = 4$

Step 2

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

$2 b + 11 = \pm 4$

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.

$2 b + 11 = 4$

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

Subtract $11$ from both sides of the equation.

$2 b = 4 - 11$

Subtract $11$ from $4$ .

$2 b = - 7$

Divide each term in $2 b = - 7$ by $2$ and simplify.

Divide each term in $2 b = - 7$ by $2$ .

$\frac{2 b}{2} = \frac{- 7}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 b}{2} = \frac{- 7}{2}$

Divide $b$ by $1$ .

$b = \frac{- 7}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$b = - \frac{7}{2}$

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

$2 b + 11 = - 4$

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

Subtract $11$ from both sides of the equation.

$2 b = - 4 - 11$

Subtract $11$ from $- 4$ .

$2 b = - 15$

Divide each term in $2 b = - 15$ by $2$ and simplify.

Divide each term in $2 b = - 15$ by $2$ .

$\frac{2 b}{2} = \frac{- 15}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 b}{2} = \frac{- 15}{2}$

Divide $b$ by $1$ .

$b = \frac{- 15}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$b = - \frac{15}{2}$

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

$b = - \frac{7}{2}, - \frac{15}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$b = - \frac{7}{2}, - \frac{15}{2}$

Decimal Form:

$b = - 3.5, - 7.5$

Mixed Number Form:

$b = - 3 \frac{1}{2}, - 7 \frac{1}{2}$

Solve the Absolute Value Inequality for b 4=|2b+11|

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