If |x| is never = to negative number then why in the algebraic equation with || (absolute vale) we have 2 solutions negative and positive?

GRE Quant Problem Solving
1

If the absolute value |x| is never equal to a negative number, why does the algebraic equation involving absolute values, such as ||, have two solutions—one positive and one negative? For example:

|4x + 9| = 21

Why does this equation have two solutions, including a negative one?

  1. 4x + 9 = 21
  2. 4x + 9 = -21

Why do we have a negative solution when the absolute value is always positive?

2

I think you might misunderstand the concept of absolute value.

Here is the definition: The absolute value of a number measures its distance from 0 on the number line.

4x+9= −21 doesn’t mean the absolute value equals −21, because its absolute value could still equal 21

Think of it like this:

|−21| = 21

In other words, even though the inside (−21) is negative, the absolute value (the output) is positive.

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