Question

Is \( |x - 2|<1 \)?
A. \( |x|<1 \)
B. \( |x - 1|<2 \)

• A. The question can be answered by one of the statements alone but not by the other.
• B. The question can be answered by using either statement alone.
• C. The question can be answered by using both the statements together, but cannot be answered by using either statement alone.
• D. The question cannot be answered even by using both statements together.

Hint:

When solving absolute value inequalities, isolate the absolute value expression and solve for the variable.

Answer 1

The Correct Option is B

We are given \( |x - 2|<1 \). This means that \( x \) is within 1 unit of 2, so \( 1<x<3 \). The correct inequality is satisfied for values of \( x \) between 1 and 3.