Solve the following inequalities and write the solution set using int

1.	Solve the following inequalities and write the solution set using interval notation.x2 – x > 20
Answer» x² – x > 20 ∴ x² – x – 20 > 0 ∴ x² – 5x + 4x – 20 > 0 ∴ (x – 5) (x + 4) > 0 ∴ either x – 5 > 0 and x + 4 > 0 or x – 5 < 0 and x + 4 < 0 Case I: x – 5 > 0 and x + 4 > 0 ∴ x > 5 and x > -4 ∴ x > 5 ….(i) Case II: x – 5 < 0 and x + 4 < 0 ∴ x < 5 and x < -4 ∴ x < -4 …..(ii) From (i) and (ii), we get x ∈ (-∞, – 4) ∪ (5, ∞)

Solve the following inequalities and write the solution set using interval notation.x2 – x > 20

Answer»

x² – x > 20

∴ x² – x – 20 > 0

∴ x² – 5x + 4x – 20 > 0

∴ (x – 5) (x + 4) > 0

∴ either x – 5 > 0 and x + 4 > 0 or x – 5 < 0 and x + 4 < 0

Case I: x – 5 > 0 and x + 4 > 0

∴ x > 5 and x > -4

∴ x > 5 ….(i)

Case II: x – 5 < 0 and x + 4 < 0

∴ x < 5 and x < -4 ∴ x < -4 …..(ii)

From (i) and (ii), we get

x ∈ (-∞, – 4) ∪ (5, ∞)