Question

Solve the inequation:
|2x + 7| ≤ 25

Answer 1

|2x + 7| ≤ 25
We know that |x| ≤ k implies – k ≤ x ≤ k
|2x + 7| ≤ 25 implies – 25 ≤ 2x + 7 ≤ 25
Thus, we have
– 25 ≤ 2x + 7 ≤ 25
Subtracting 7 from both sides, we get
– 32 ≤ 2x ≤ 18
Dividing by 2 on both sides, we get
− 16 ≤ x ≤ 9
∴ x can take all real values between − 16 and 9 including − 16 and 9.
∴ the solution set is [− 16, 9].