## Intermediate Algebra for College Students (7th Edition)

$(1,3)$
We are asked to solve the absolute value inequality: $|x-2|\lt 1$ We remove the absolute value sign by splitting the inequality into two as follows: $-1 \lt x-2 \lt 1$ We solve for $x$ by adding $2$: $-1+2 \lt x-2+2 \lt 1+2$ $1 \lt x \lt 3$ In interval notation, this can be written as: $(1,3)$ See the number line graph below.