91Ó°ÊÓ

The solution of the given inequality $\left|3d−1\right|≤8$is:

Case 1: $3d−1$is non-negative.

$\begin{array}{c}3d−1≤8\\ 3d−1+1≤8+1\\ 3d≤9\\ \frac{3d}{3}≤\frac{9}{3}\\ d≤3\\ d∈\left(−∞,3\right]\end{array}$

Case 2: $3d−1$is negative.

$\begin{array}{c}−\left(3d−1\right)≤8\\ \left(−1\right)\left(−\left(3d−1\right)\right)â‰\yen \left(−1\right)\left(8\right)\\ 3d−1â‰\yen −8\\ 3d−1+1â‰\yen −8+1\\ 3dâ‰\yen −7\\ \frac{3d}{3}â‰\yen \frac{−7}{3}\\ dâ‰\yen −\frac{7}{3}\\ d∈\left[−\frac{7}{3},∞\right)\end{array}$

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$3d−1≤8$ and$3d−1â‰\yen −8$ to find the solution of the inequality $\left|3d−1\right|≤8$.

The intersection of the solutions of the inequalities$3d−1≤8$and $3d−1â‰\yen −8$is:

$d∈\left[−\frac{7}{3},3\right]$

Therefore, the solution of the inequality$\left|3d−1\right|≤8$ is $d∈\left[−\frac{7}{3},3\right]$.

The graph of the solution set which is$d∈\left[−\frac{7}{3},3\right]$ is: