Inequalities Question 6

The set of all values $x$ that satisfies $|x-2|\lt 7$ is the same as the set of all values of $x$ that satisfies:

0 \lt x \lt 5

0 \lt x \lt 9

-5 \lt x \lt 5

-5 \lt x \lt 9

-9 \lt x \lt 9

Approach

|x-2|\lt 7

x-2\lt 7

x \lt 9

x-2\gt -7

x \gt -5

\boxed{-5\lt x \lt 9}