91Ó°ÊÓ

The solution of the given inequality$\left|2c+3\right|≤11$ is:

Case 1:$2c+3$ is non-negative.

$\begin{array}{c}2c+3≤11\\ 2c+3−3≤11−3\\ 2c≤8\\ \frac{2c}{2}≤\frac{8}{2}\\ c≤4\\ c∈\left(−∞,4\right]\end{array}$

Case 2:$2c+3$ is negative.

$\begin{array}{c}−\left(2c+3\right)≤11\\ \left(−1\right)\left(−\left(2c+3\right)\right)â‰\yen \left(−1\right)\left(11\right)\\ 2c+3â‰\yen −11\\ 2c+3−3â‰\yen −11−3\\ 2câ‰\yen −14\\ \frac{2c}{2}â‰\yen \frac{−14}{2}\\ câ‰\yen −7\\ c∈\left[−7,∞\right)\end{array}$

The solution of the inequality$\left|x\right|≤a$ is$xâ‰\yen −a$ and $x≤a$.

That implies the solution of the inequality$\left|x\right|≤a$ is the intersection of the solutions of the inequalities$xâ‰\yen −a$ and $x≤a$.

Find the intersection of the solutions of the inequalities$2c+3≤11$ and $2c+3â‰\yen −11$to find the solution of the inequality $\left|2c+3\right|≤11$.

The intersection of the solutions of the inequalities$2c+3≤11$ and$2c+3â‰\yen −11$ is:

$c∈\left[−7,4\right]$

Therefore, the solution of the inequality$\left|2c+3\right|≤11$ is $c∈\left[−7,4\right]$.

The graph of the solution set which is$c∈\left[−7,4\right]$ is: