Question

Solve the inequation $-8\frac{1}{2}<-\frac{1}{2}-4x\le 7\frac{1}{2}$, $x\in I$ and represent the solution set on the number line.

Answer 1

Step 1: Solve the inequation

$$\begin{gathered} -8\frac{1}{2}<-\frac{1}{2}-4x\le 7\frac{1}{2} \\ -\frac{17}{2}<-\frac{1}{2}-4x\le \frac{15}{2} \end{gathered}$$

Multiply 2 to both sides

$$\begin{gathered} -17<-1-8x\le 15 \\ -16<-8x\le 16 \\ 2>x\ge -2 \end{gathered}$$

Step 2: Representation on number line

The solution set will be $-2\le x<2$, so the solution set will be $x=\{-2,-1,0,1\}$ on the number line will

Hence the solution set of the inequality $-8\frac{1}{2}<-\frac{1}{2}-4x\le 7\frac{1}{2}$ is $-2\le x<2$ and the representation of the solution set on the number line is as shown above.