Answer: x = 2.
- A x <= 1 or x >= 2
- B 1 <= x <= 2
- C x < 1 or x > 2 only
- D No solution
Correct answer: A. x <= 1 or x >= 2
Explanation: Sign-rule method: critical points x=1 and x=2 divide the number line into three intervals. Test each: x<1: (-)(-) =+≥0 ✓; 1<x<2: (+)(-) =-<0 ✗; x>2: (+)(+)=+≥0 ✓. Include endpoints (equality holds). Answer: x ≤ 1 or x ≥ 2
One-variable inequalities use open (excluded) or closed (included) circles on a number line; two-variable inequalities use a dashed (strict) or solid (non-strict) boundary line, with the solution being the entire shaded half-plane on one side of it.
Concept context
Solving linear inequalities in one and two variables algebraically and graphically, and representing solutions on a number line or as a region in a plane.