Question

The IQ scores of the middle 50% of a population can be written as

I

100

15

where x is a person's IQ. Solve the inequality to find the IQ scores for the middle 50% of the population.

x 270 and x s 130

Ox570 and x 2 130

Oxs 90 and x 2 110

x 290 and x s 110

Answer 1

Complete question :

The IQ scores of the middle 50% of a population can be written as (x - 100) / 15 ≤ 2/3

Answer: 90 ≤ x ≤ 110

Oxs 90 and x 2 110

Explanation:

Given the inequality:

The middle 50% of the population :

(x - 100) / 15 ≤ 2/3

The upper bound :

(x - 100) / 15 ≤ 2/3

multiply both sides by 15

(x - 100) / 15 * 15 ≤ 2/3 * 15

(x - 100) ≤ 2/3 * 15

x - 100 ≤ 10

x ≤ 10 + 100

x ≤ 110

The lower bound :

- (x - 100) / 15 ≤ 2/3

(-x + 100) / 15 ≤ 2/3

multiply both sides by 15

(-x + 100) / 15 * 15 ≤ 2/3 * 15

(-x + 100) ≤ 2/3 * 15

-x + 100 ≤ 10

-x ≤ 10 - 100

-x ≤ - 90

x ≤ 90

90 ≤ x ≤ 110