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

$- 1 < x < 13$
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 $- 1 < x < 13$.