Question

Express the set of numbers, x, satisfying |5x-1|-2<12 as an interval. Write your answer using interval notation.

Answer 1

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).