Question

Solve |x| < 5 A{x|-5 < x < 5} B{x|x < -5 or x > 5} C{-5, 5}

Answer 1

When solving an absolute value inequality,

you can split the problem up into two separate inequalities.

The first inequality will look just like the original problem,

minus the absolute value signs (x < 5).

In the second inequality, you must switch the direction

of the inequality sign and make the right side negative (x > -5).

The word “and” is used between the two inequalities when

we  split things up, in this case x < 5 and x > -5.

The word "and" means intersection which means where the graphs overlap.

In this case, that's less than 5 and greater than -5.

In set notation, this reads {x: -5 < x < 5}.