Question

Identify the interval notation that represents the solution of|3x - 15| le 30).

a)(-5, 15]
b)[-5, 15]
c)[-3, 13]
d)(5, 15]

Answer 1

The inequality |3x - 15| ≤ 30 is solved by splitting it into two separate inequalities, 3x - 15 ≤ 30 and 3x - 15 ≥ -30. Solving these, we get the compound inequality -5 ≤ x ≤ 15, which is represented by the interval notation [-5, 15].

Step-by-step explanation:

To solve the inequality |3x - 15| ≤ 30, we need to split this into two separate inequalities:

1. 3x - 15 ≤ 30
2. -(3x - 15) ≤ 30, which is the same as 3x - 15 ≥ -30

Let's solve both inequalities:

1. 3x ≤ 45
   x ≤ 15
2. 3x ≥ -15
   x ≥ -5

Combining the two inequalities gives us the solution -5 ≤ x ≤ 15, which in interval notation is [-5, 15]. So the correct answer is option b.