Question

Solve the inequation$-3+x\le \frac{8x}{3}+2\le \frac{14}{3}+2x,x\in I$ and represent the solution set on the number line.

Answer 1

Step 1 (Solve the inequation):

$-3+x\le \frac{8x}{3}+2\le \frac{14}{3}+2x,x\in I$

multiply 3 to both sides

$$\begin{gathered} -9+3x\le 8x+6\le 14+6x \\ -9+3x\le 8xand8x+6\le 14+6x \\ -9-6\le 5xand2x\le 8 \\ x\ge \frac{-15}{5}andx\le 4 \\ x\ge -3andx\le 4 \end{gathered}$$

Step 2 (Representing the solution set on the number line):

The solution set will be$x\in \{-3,-2,-1,0,1,2,3,4\}$, so the solution set on the number line will be

Hence the solution set of the inequality $-3+x\le \frac{8x}{3}+2\le \frac{14}{3}+2x,x\in I$ is$x\in \{-3,-2,-1,0,1,2,3,4\}$ and the representation of the solution set on the number line is as shown above.