Answer:
Given inequality,
[tex]\frac{3}{4}|x+8|>\frac{1}{2}|2x+10|[/tex]
[tex]\implies \frac{6}{4}|x+8|>|2x+10|[/tex]
[tex]\frac{3}{2}|x+8|>|2x+10|[/tex]
[tex]\frac{3}{2}(x+8)>\pm (2x+10)[/tex]
[tex]\frac{3}{2}(x+8)>(2x+10)\text{ and }\frac{3}{2}|x+8|>-(2x+10)[/tex]
[tex]3(x+8)>4x+20\text{ and }3(x+8)>-4x-20[/tex]
[tex]3x+24>4x+20\text{ and }3x+24>-4x-20[/tex]
[tex]3x-4x>20-24\text{ and }3x+4x>-20-24[/tex]
[tex]-x>-4\text{ and }7x>-44[/tex]
[tex]\implies x < 4\text{ and }x>-\frac{44}{7}[/tex]
[tex]\implies (-\frac{44}{7}, 4)[/tex]
Which is the required solution of the inequality, shown in the graph.
