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And represents the distance between a and 0 on a number line. Has two solutions x = a and x = -a because both numbers are at the distance a from 0. This holds true for all absolute value inequalities. ... Because by definition, the absolute value of a number is its distance from 0 on a number line which means that there are two such numbers: a positive/negative number
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Why the solution for an absolute value equation or inequality typically result in a pair of equations or inequalities?

Because the absolute value equations behave differently in the different ranges.

For a given absolute value equation (or inequality)

| x - a| = b

We get two equations or inequalities:

x - a = b

x - a = - b

And this is why the solution leads to two equations, this originates in the fact that the parent absolute value function:

f(x) = |x|

Behaves differently if x is positive or negative.

  • f(x) = x if x > 0
  • f(x) = -x if x < 0

If you want to learn more, you can read:

https://brainly.com/question/17654897