Question

Which of the following is equivalent to $|x-3|<2$?

• A. x > 1
• B. x < 5
• C. 1 < x <5
• D. x > -1

Answer 1

The correct option is C 1 < x <5

We know that if $|x|<a$, then we can write it as $–a<x<a$
Therefore $|x-3|<2$ can be written as $-2<x-3<2$
Add 3 on each side
$-2+3<x-3+3<2+3$
$1<x<5$
The correct answer is option C.