Which values of X will be nearer to the point A = -4 than to the point B = 8 on the number line?

Correct answer marked below

0 < x < 3

2 < x < 2.5

x < -9

Correct

Both I and III

Both II and III

You can see the correct answer above. Sign in for free to unlock the complete worked solution.

Get detailed analytics, unlock full explanations, and move up difficulty tiers as you practice.

Explanation

Preview

Official Explanation

Official

To determine when x is closer to -4 than to 8, we set up the inequality

|x-(-4)|<|x-8|

, which simplifies to

|x+4|<|x-8|

. Since both sides are non-negative, we can square both sides:

x^2+8x+16<x^2-16x+64

. This…

Comments

IApr 29, 2025

can you explain more?

LakshayMar 17, 2025

thanks for posting

What this question tests

Your ability to solve absolute-value equations and inequalities by considering both cases.

Dropping the absolute value bars entirely or missing that |x| = k has two solutions when k > 0.