Question

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

Answer 1

Given inequality,

`(3)/(4)|x+8|>(1)/(2)|2x+10|`

`\implies (6)/(4)|x+8|>|2x+10|`

`(3)/(2)|x+8|>|2x+10|`

`(3)/(2)(x+8)>\pm (2x+10)`

`(3)/(2)(x+8)>(2x+10)\text{ and }(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>-(44)/(7)`

`\implies (-(44)/(7), 4)`

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