Answer: x > 2.
- A x > 2
- B x < 2
- C x > 0
- D x < 0
Correct answer: A. x > 2
Explanation: Since the numerator is 1 (positive constant), the fraction 1/(x-2) is positive iff the denominator (x-2) is positive. So x-2 > 0, which gives x > 2. Check: x=3: 1/1=1>0 ✓; x=1: 1/(-1)=-1<0 ✗. Answer: 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.