Question

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Answer 1

Forget about the absolute value part for a second...

if x + 3 < 5, then x must be less than 2, right?

You can isolate x by subtracting 3 from both sides...
x + 3 < 5
x < 2

But when x+3 is negative, then you do need to worry about the absolute value, since after the absolute value, it still must be less than 5.

x must be larger than -8, because when you add 3, you need to get a number greater than -5 so the absolute value will make the whole thing less than 5.

-8 < x < 2
It sounds confusing, but just try a couple x values above and below -8 and 2 to see how it makes the inequality work or not work.

Answer 2

I like to think of these this way:
\[ \large |x + 3| < 5 \\ \ \\ \textrm{is the same as} \\ \ \\ \large x + 3 < 5 \ \textrm{and} \\ \large -(x+3) > 5\]

This works because when