Question

Solve the following linear inequations and graph the solution set on a real number line.
$3x–9\le 4x–7<2x+5,x\in R$

Answer 1

Finding the solution set of $x$
Given:
$3x–9\le 4x–7<2x+5,x\in R$
By taking the like terms to one side of equation,we get
$4x-3x\ge -9+7$
$x\ge -2$
Now,consider $4x-7<2x+5$
By transposing we get,
$4x-2x<5+7$
$2x<12$
$x<\frac{12}{2}$
$x<6$
As per the condition given in the question, $x\in R$
Therefore, the solution set is $x=\{-2\le x<6\}$
Set can be represented in number line as.