Question

Graph the solution of this inequality 3/4|(x+8)>|1/2|(2x+10)|

Answer 1

Answer:

Given inequality,

$\frac{3}{4}|x+8|>\frac{1}{2}|2x+10|$

$\implies \frac{6}{4}|x+8|>|2x+10|$

$\frac{3}{2}|x+8|>|2x+10|$

$\frac{3}{2}(x+8)>\pm (2x+10)$

$\frac{3}{2}(x+8)>(2x+10)\text{ and }\frac{3}{2}|x+8|>-(2x+10)$

$3(x+8)>4x+20\text{ and }3(x+8)>-4x-20$

$3x+24>4x+20\text{ and }3x+24>-4x-20$

$3x-4x>20-24\text{ and }3x+4x>-20-24$

$-x>-4\text{ and }7x>-44$

$\implies x < 4\text{ and }x>-\frac{44}{7}$

$\implies (-\frac{44}{7}, 4)$

Which is the required solution of the inequality,  shown in the graph.

Answer 2

I graphed this out for you, I hope it helps! :)