Question

Solve |y - 2|<10

A.) y
B.) -12 < y < 8
C.) -8 < y < 8

Answer 1

OPTION A

Explanation:

We have:
`$ |x - a| < b \implies - b < x - a < b $`

Adding 'a' to the components:

- b + a < x < b + a

This is the result.

Here, we have: |y - 2| < 10

⇒ -10 < y - 2 < 10

Adding 2, we get:

- 10 + 2 < y < 10 + 2

⇒ - 8 < y < 12

That is, 'y' can take any value between -8 and 12.

In set notation: {y : - 8 < y < 12} : OPTION A is the answer.