Question

Which conjunction or disjunction is equivalent to the following inequality?

|a - 9| ≤ 4

a - 9 ≤ 4 AND a - 9 ≤ - 4

a - 9 ≤ 4 AND a - 9 ≥ - 4

a - 9 ≤ 4 OR a - 9 ≤ - 4

a - 9 ≤ 4 OR a - 9 ≥ - 4

Answer 1

a - 9 ≤ 4 and a - 9 ≥ - 4

Explanation:

Answer 2

Use the general definition:

|x - a| ≤ k => - k ≤ x - a ≤ k

So, |a - 9| ≤ 4 => - 4 ≤ a - 9 ≤ 4

Which is a - 9 ≥ - 4 and a - 9 ≤ 4.

That is the second option.

Answer: a - 9 ≤ 4 and a - 9 ≥ - 4