Final answer:
To solve the inequality |5x-1|-2<12 and express the set of numbers x that satisfy it as an interval, isolate the absolute value expression, break it into two separate inequalities, solve for x in each inequality, and represent the solution as an interval (-13/5,3).
Step-by-step explanation:
To solve the inequality |5x-1|-2<12, we first isolate the absolute value expression by adding 2 to both sides:
|5x-1|<14
Now, we break it down into two separate inequalities:
5x-1<14 and -(5x-1)<14
For the first inequality, we solve for x:
5x<15
x<3
For the second inequality, we solve for x:
5x-1>-14
5x>-13
x>-13/5
Therefore, the set of numbers x that satisfy |5x-1|-2<12 can be expressed as an interval notation: (-13/5,3).