I am learning the topic of solving absolute value inequality question. I had mostly understood the steps in order to solve for an inequality. However, I'm still clueless of a step to solve the inequality below:
Which is: Why does $ 3-x \ge 0$? I notice that 3-x is clearly not inside a radical, so it shouldn't have that requirement. Am I right?
Best Answer
Solve two separate cases.
Case 1: $x \ge 1$. Then solve $x-1 \ge 3-x$ to get $x \ge 2$.
Case 2: $x < 1$. Then solve $1-x \ge 3-x$ which is never true.
Hence the solution is $x \ge 2$.