Solve the following inequalities and write the solution set using int

1.	Solve the following inequalities and write the solution set using interval notation.6x2 + 1 ≤ 5x
Answer» 6x² – 5x + 1 ≤ 0 6x² – 3x – 2x + 1 ≤ 0 (3x – 1) (2x – 1) ≤ 0 either 3x – 1 ≤ 0 and 2x – 1 ≥ 0 or 3x – 1 ≥ 0 and 2x – 1 ≤ 0 Case I: 3x – 1 ≤ 0 and 2x – 1 ≥ 0 ∴ x ≤ 1/3and x ≥ 1/2, which is not possible. Case II: 3x – 1 ≥ 0 and 2x – 1 ≤ 0 ∴ x ≥ 1/3 and x ≤ 1/2 ∴ x ∈ [1/3, 1/2]

Solve the following inequalities and write the solution set using interval notation.6x2 + 1 ≤ 5x

Answer»

6x² – 5x + 1 ≤ 0

6x² – 3x – 2x + 1 ≤ 0

(3x – 1) (2x – 1) ≤ 0

either 3x – 1 ≤ 0 and 2x – 1 ≥ 0 or 3x – 1 ≥ 0 and 2x – 1 ≤ 0

Case I:

3x – 1 ≤ 0 and 2x – 1 ≥ 0

∴ x ≤ 1/3and x ≥ 1/2, which is not possible.

Case II:

3x – 1 ≥ 0 and 2x – 1 ≤ 0

∴ x ≥ 1/3 and x ≤ 1/2

∴ x ∈ [1/3, 1/2]