Q56. - Algebra 1

Question

Solve each equation. 

$\left|b+9\right|=2$

Step-by-Step Solution

Answer

The solution set will be $b=-7\text{ and }b=-11$.

Step 1. Use the definition of the absolute value function.

The absolute value or modulus of a real number x denoted |x| is the non-negative value of x without regard to its sign.

Absolute value refers to a point's distance from zero or origin on the number line, regardless of the direction. 

Step 2. Solve for the first possible solution.

We are given the expressions: $|b+9|=2$

Since an absolute function value can never be negative we have two scenarios that are possible. 

Case: 1 when expression inside the modulus sign is negative, that is 

$\begin{array}{l} -(b+9)=2\text{\hspace{0.33em} [Distribute]}\\ -b-9=2\\ -b-9+9=2+9\text{ [Add 9 to both sides]}\\ -b=11\\ -b\times \left(-1\right)=11\times \left(-1\right)\text{ [multiply by -1 both sides]}\\ b=-11\end{array}$

Step 3. Solve for a second possible solution.

We are given the expressions:  $|b+9|=2$

Case: 2 when expression inside the modulus sign is positive, that is

  $\begin{array}{l} b+9=2\\ b+9-9=2-9\text{ [Add -9 to both sides]}\\ b=-7\end{array}$

Hence, the solution set will be $b=-7\text{ and }b=-11$.