Solve \( |x-3|-2 \leq 0 \) \( \begin{array}{l}1 \leq x \leq 5 \\ --2

Ask by Malone Ray. in the United States

Feb 03,2025

To solve the inequality \( |x-3|-2 \leq 0 \), we start by isolating the absolute value: \[ |x-3| \leq 2 \] This means that the expression inside the absolute value, \(x-3\), must satisfy the range: \[ -2 \leq x - 3 \leq 2 \] We can break this into two inequalities: 1. \(x - 3 \geq -2 \implies x \geq 1\) 2. \(x - 3 \leq 2 \implies x \leq 5\) Combining these results, we find: \[ 1 \leq x \leq 5 \] So the solution to the inequality \( |x-3|-2 \leq 0 \) is \(x\) in the interval \([1, 5]\). However, consider the other options you presented: 1. --2