Question

Solve the following inequalities and represent the solution on a number line:
`(3x)/(2) + (1)/(4) > (5x)/(8) - (1)/(2)`

Answer 1

The given inequality is
`(3x)/(2) + (1)/(4) > (5x)/(8) - (1)/(2)`

⇒ `(3x)/(2) - (5x)/(8) > -(1)/(2) - (1)/(4)`

⇒ `(12x - 5x)/(8) > (-2 -1)/(4)`

⇒ `(7x)/(8) >(-3)/(4)`

⇒ 4(7x) > -3 x 8
⇒ 28x > -24
⇒ x > `(-24)/(28)`
⇒ x > -6/7
The graph of the solution set is x > -6/7.