Question

Find the complete solution set to the inequality $|x|+|x-3|>3$.

• A. $\{x:x>3orx<0\}$
• B. $\{x:-3<x<3\}$
• C. $\{x:-3>x\}$
• D. $\{x:-3<x\}$
• E. $\{x:\text{The set of all real numbers}\}$

Answer 1

The correct option is A $\{x:x>3orx<0\}$

Given, $|x|+|x-3|>3$
For $x<0$ , we have $-x+3-x>3$ , which implies $x<0$
For $0<x<3$ , we have $x+3-x>3$ , which implies $3>3$ (false)
For $x>3$ , we have $x+x-3>3$ , which implies $x>3$
Therefore, the values of $x$ are $x>3$ and $x<0$.