Question

Which absolute value equation represents the number line?

A) -|x - 2| = 5
B) |x - 2| = -5
C) -|x| - 2 = 5
D) -|x - 2| = -5

Answer 1

The correct answer is -|x - 2| = -5

Answer 2

D

Explanation:

A is impossible.

the absolute value of something is always a positive number. the negative sign before it makes it an always negative number. so, this can never be equal to +5.

B is impossible for the same reasons.

the absolute value is always positive and can never be equal to -5.

C is impossible again for the same reasons.

the negative absolute value of x is always negative. subtracting 2 from that makes the result even more negative. this can never be equal to +5.

D is the only fitting option.

we have two extreme points x = -3 and x = 7.

putting them into the equation gives us for x = -3

-|-3 - 2| = -|-5| = -5 => correct

and for x = 7

-|7 - 2| = -|5| = -5 => correct