Question

If the inequality -13 ≤ x ≤ 5 is expressed in the form |x-a|≤b, then the values of a and b are respectively

• A. 4,8
• B. -4,9
• C. 4,9
• D. 5,9
• E. -5,9

Answer 1

The Correct Option is B

Given inequality: 

-13 ≤ x ≤ 5

Goal: Express this inequality in the form |x - a| ≤ b, and find the values of a and b.

Step 1: Understand the form |x - a| ≤ b.

The inequality |x - a| ≤ b means that x lies within a distance of b from a. This can be rewritten as:

-b ≤ x - a ≤ b

or equivalently:

a - b ≤ x ≤ a + b

Step 2: Compare the given inequality with the desired form.

We are given -13 ≤ x ≤ 5. We need to express this as x being within a certain distance from a center value. The middle of the interval [-13, 5] is:

a = (−13 + 5) / 2 = −8 / 2 = −4

Step 3: Find b.

The distance from the center value a = -4 to the endpoints is:

b = |5 - (-4)| = |5 + 4| = 9

Step 4: Conclusion.

The values of a and b are -4 and 9, respectively.