Question

|2x − 1| < 11 express the solution in set-builder notation

Answer 1

We have - 11 < 2x - 1 < + 11 ;/ +1;
Then, - 10 < 2x < 12 ; / ÷ 2;
- 5 < x < 6;

Answer 2

x

Explanation:

Let's remember that |x| = 11 means that the distance from x to 0 is 11, i.e. x = 11 or x = -11.

In this case we have an inequality, |2x - 1| < 11. That means that the distance from 2x-1 to 0 is less than 11.

So, - 11 < 2x - 1 < 11

We need to find out the value of x, so first we sum 1 in each part of the inequality:

-11 + 1 < 2x - 1 + 1 < 11 + 1

-10 < 2x < 12

Now we divide by 2:

-10/2 < 2/2x < 12/2

-5 < x < 6

The solution we are looking for is -5 < x < 6