Question

What are the solutions to the absolute value inequality |x − 70| ≤ 3?

Remember, the inequality can be written as −3 ≤ x − 70 ≤ 3

or as x − 70 ≤ 3 and x − 70 ≥ −3.

Answer 1

67 ≤ x ≤ 73

Explanation:

The absolute value of a real number x is the non negative value of x. Therefore the absolute value of x (|x|) = x for x ≥ 0 and -x for x < 0.

An expression |x - a| = b signifies that x - a = b or -(x - a) = b

Given that |x − 70| ≤ 3, hence:

|x − 70| ≤ 3

x - 70 ≤ 3 or -(x - 70) ≤ 3

x ≤ 3 + 70 or x - 70 ≥ -3

x ≤ 73 or x ≥ -3 + 70

x ≤ 73 or x ≥ 67

67 ≤ x ≤ 73

Hence the solution of |x − 70| ≤ 3 is 67 ≤ x ≤ 73