Question

Solve the following inequation and write the solution set :
$13x-5<15x+4<7x+12,xϵR$
Represent the solution on a real number line.
[3 MARKS]

Answer 1

Solving each inequation: 1 Mark
Representation of solution on the graph: 1 Mark

Given $13x-5<15x+4<7x+12,xϵR$
$\Rightarrow 13x-5<15x+4\Rightarrow -5-4<15x-13x\Rightarrow -9<2x\Rightarrow -\frac{9}{2}<x$
Also, 15x + 4 < 7x + 12
$\Rightarrow 15x-7x<12-4\Rightarrow 8x<8$
$\Rightarrow x<1$
Solution set - $\{x:-4\frac{1}{2}<x<1,xϵR\}$
The solution set is represented on the number line as given in the following: