Question

The minimum score on the SAT test is 600 and the maximum score is 2400. Write an absolute value equation that represents the minimum and maximum scores. Use x to represent the scores.

Answer 1

The inequality

|x-a| ≤ b

Which means

-b ≤ x-a ≤ b

Adding a on all sides we get

a-b ≤ x ≤ a+b

Here

The minimum score is 600 & the maximum score is 2400

So we have

600 ≤ x ≤ 2400

Comparing with

a-b ≤ x ≤ a+b

We get

a-b = 600

a+b = 2400

Adding them we get

2a = 3000

a = 1500

Substituting the value of a in

a-b = 600

we get

1500 - b = 600

b = 900

So we have

|x - 1500| ≤ 900

This is the required in equality.