Answer:
[tex]x > -1[/tex] or
[tex]x > 2[/tex] or
[tex]x > 3[/tex]
Step-by-step explanation:
Given
[tex](x + 1)(x - 2) (x - 3) > 0[/tex]
Required
Solve; with steps
[tex](x + 1)(x - 2) (x - 3) > 0[/tex]
Start by splitting the inequality as follows
[tex]x + 1 > 0[/tex] or [tex]x - 2 > 0[/tex] or [tex]x - 3 > 0[/tex]
Solve the inequalities one after the other
Solving: [tex]x + 1 > 0[/tex]
Subtract 1 from both sides
[tex]x + 1 - 1 > 0 - 1[/tex]
[tex]x > -1[/tex]
Solving: [tex]x - 2 > 0[/tex]
Add 2 to both sides
[tex]x - 2 +2 > 0 +2[/tex]
[tex]x > 2[/tex]
Solving: [tex]x - 3 > 0[/tex]
Add 3 to both sides
[tex]x - 3 +3> 0+3[/tex]
[tex]x > 3[/tex]
Hence, the solution to the inequality is
[tex]x > -1[/tex] or
[tex]x > 2[/tex] or
[tex]x > 3[/tex]
