Find Domain (Solve Inequality)

Question

Given inequality

2x³-x²-3x > 0

Answer 1

Given inequality is 2x³-x²-3x > 0

2x³-x²-3x > 0

Take out common term x

x (2x ²- x - 3) > 0

x > 0 and (2x ²- x - 3) > 0

(2x ²- x - 3) > 0

(2x ²- 3x + 2x - 3) > 0

Take out common factors.

x (2x - 3) +1(2x - 3 ) > 0

Take out common factors.

(x + 1)(2x - 3) > 0

x + 1 > 0 or 2x - 3 > 0

x + 1 > 0

Subtract 1 from each side.

x > -1

And 2x - 3 > 0

Add 3 to each side

2x > 3

Divide each side by 2.

x > 3/2

There fore x > 0, x > -1 and x > 3/2

graph the solution on number line.