Question

Solve each equation. Then graph the solution set.

$|2b+5|=9$

Short answer

The solution set of the equation is$\{2,-7\}.$

The graph of the solution set is:

Step-by-step solution

Step 1. Given information.

We have an equation $|2b+5|=9$.

To find the value of$b$ and plot the graph of solution.

Step 2. Apply concept.

We apply the concept of modulus function.

As$\left|x\right|=\left\{\begin{array}{c}xifx\le 0\\ -xifx>0\end{array}\right.$

Step 3. Calculation.

Here will exist two cases for the modulus function:

$\begin{array}{l}Case1:\\ 2b+5=9\\ 2b=9-5\\ 2b=4\\ b=\frac{4}{2}\\ b=2\\ Case2:\\ 2b+5=-9\\ 2b=-9-5\\ 2b=-14\\ b=\frac{-14}{2}\\ b=-7\end{array}$

Hence, the solution set of the given expression is$\{2,-7\}.$

The graph of the solution set is: