Question

What is the solution set for `abs(x – 6) + 3 < 10`?

Answer 1

`-1 < x < 13`

Explanation:

First, subtract 3 from both sides of the inequality `|x-6|+3 < 10` to get `|x-6| < 7`. Next, note that this inequality implies that `-7 < x-6 < 7`. Finally, add 6 to each part of this line of inequalities to get `-1 < x < 13`.

Another way to think about the inequality `|x-6| < 7` is that you are looking for all `x`-values whose distance to 6 is less than 7. If you draw a number line, that will help you see the answer is `-1 < x < 13`.