Question

Express the phrase as an inequalities involving an absolute value 1. All real numbers x less than 3 units from 0 . 2. All real numbers x at most 4 units from 2 .

Answer 1

To express the phrase as absolute value inequalities, |x - 0| < 3 and |x - 2| ≤ 4 can represent the given conditions.

Step-by-step explanation:

To express the phrase using absolute value inequalities, we need to consider two cases:

1. For all real numbers x less than 3 units from 0, we can write the inequality as |x - 0| < 3. This means that the distance between x and 0 should be less than 3, which can be expressed as -3 < x < 3.
2. For all real numbers x at most 4 units from 2, we can write the inequality as |x - 2| ≤ 4. This means that the distance between x and 2 should be at most 4, which can be expressed as -4 ≤ x - 2 ≤ 4.