Question

What is the solution set for |x - 6| + 3 < 10?
Choose one answer.
a. x > 1 or x < -13
b. x < -1 and x > 13
c. x > -1 and x < 13
d. x < 13 or x > -13

Answer 1

C. Because when you substract 3 from 10 you get 7. 7 plus 6 = 13. The sign stays the same because you didn't divide by a negative. x has to stay greater than -1 because of its absolute value.

Answer 2

|x - 6| < 7 (subtract 3 from both sides)
-7 < x - 6 < 7 (Deal with absolute values bars and add 6 to all three sides)
-1 < x < 13

So, yes, the answer is c.