Squaring inequalities question

[yo4561]

Hello!

I have a question on the following example in the All the Quant book:
x^2 < 4

The answer is then x<2 and x>-2.

To clarify, this is not a combined inequality where the answer is -2<x<2, right? Instead, the answer saying when x is positive --> x <2 and when x is negative x>-2?

Many thanks in advance my MP friends

[esledge]

I have a question on the following example in the All the Quant book:
x^2 < 4

The answer is then x<2 and x>-2.

To clarify, this is not a combined inequality where the answer is -2<x<2, right? Instead, the answer saying when x is positive --> x <2 and when x is negative x>-2?

These are the same thing, really, so I'm not sure why you wouldn't combine into a single expression: -2<x<2.

[yo4561]

Thank you! To follow-up, how would you write the solutions to this problem (also given in the MP All the Quant guide) in the combined format which you mentioned is the same above?

10 + x^2 ≥ 19
The answer says x ≥ 3 and x ≤ -3

Many thanks for all of your help

[esledge]

That one you can't combine because x ≥ 3 and x ≤ -3 are separate, non-overlapping ranges on the number line (draw a number line and shade these areas to see that there is actually space between them).