Question

In solving the absolute value inequality |2x − 1| < 11, the solution expressed in set-builder notation is:

A) 5 < x < 6
B) x
C) x < 6
D) –6 < x < 6

Answer 1

The solution to the absolute value inequality |2x − 1| < 11 is the range -5 < x < 6 in set-builder notation, which corresponds to option D.

Step-by-step explanation:

To solve the absolute value inequality |2x − 1| < 11, we consider that the absolute value of an expression is less than a positive number will result in a range of solutions where the expression is between the negative and the positive of that number.

First, we split the inequality into two separate inequalities:

• 2x − 1 < 11 (when the expression inside the absolute value is positive or zero)
• 2x − 1 > -11 (when the expression inside the absolute value is negative)

Then solve each inequality individually:

1. Add 1 to both sides of 2x − 1 < 11: 2x < 12
2. Divide both sides by 2: x < 6
3. Add 1 to both sides of 2x − 1 > -11: 2x > -10
4. Divide both sides by 2: x > -5

Combining the solutions, we have -5 < x < 6. Therefore, the solution in set-builder notation is x, which corresponds to option D.