Question

Solve the following inequation, also write the solution set and represent it on the number line.$-3(x-7)\ge 15-7x>\frac{x+1}{3},x\in R$.

Answer 1

Step 1: Solve the inequation

$$\begin{gathered} -3(x-7)\ge 15-7x>\frac{x+1}{3},x\in R \\ -3x+21\ge 15-7x>\frac{x+1}{3} \\ 7x-3x\ge 15-21and15-7x>\frac{x+1}{3} \\ 4x\ge -6and45-21x>x+1 \\ x\ge \frac{-3}{2}and44>22x \\ x\ge \frac{-3}{2}andx<2 \end{gathered}$$

Step 2: Representation on the number line

The solution set will be, so the solution set on the number line $-\frac{3}{2}\le x<2$will be

Hence the solution set of the inequality $-3(x-7)\ge 15-7x>\frac{x+1}{3},x\in R$ is $-\frac{3}{2}\le x<2$ or $[-\frac{3}{2},2)$ and the representation of the solution set on the number line is as shown above.