Question

Solve the following inequation, 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

Given: $-3(x-7)\ge 15-7x>\frac{x+1}{3}$
$-3x+21\ge 15-7x>\frac{x+1}{3}$
$\Rightarrow -3x+21\ge 15-7x$ and $155-7x>\frac{x+1}{3}$
$\Rightarrow 4x\ge -6$ and $45-21x>x+1$

$\Rightarrow x\ge -\frac{3}{2}$ and $44>22x$

$\Rightarrow x\ge \frac{-3}{2}$ and $2>x$
$\therefore$ Solution set $=\{x:x\in R,\frac{-3}{2}\le x<2\}$