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.
