Question

Explain how to solve the inequality (x + 1)(x – 2) ∙ (x – 3) > 0. Explain in your own words, each step necessary to solve the inequality, making sure to follow the proper order of operations. Is this inequality accurate? Explain why or why not.

Answer 1

`x > -1` or

`x > 2` or

`x > 3`

Explanation:

Given

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

Required

Solve; with steps

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

Start by splitting the inequality as follows

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

Solve the inequalities one after the other

Solving:
`x + 1 > 0`

Subtract 1 from both sides

`x + 1 - 1 > 0 - 1`

`x > -1`

Solving:
`x - 2 > 0`

Add 2 to both sides

`x - 2 +2 > 0 +2`

`x > 2`

Solving:
`x - 3 > 0`

Add 3 to both sides

`x - 3 +3> 0+3`

`x > 3`

Hence, the solution to the inequality is

`x > -1` or

`x > 2` or

`x > 3`