Answer: -3 < x <= 4.
- A x < -3 or x > 4
- B -3 < x <= 4
- C -3 <= x < 4
- D x <= -3 or x >= 4
Correct answer: B. -3 < x <= 4
Explanation: Rearranging gives (x-4)/(x+3) <= 0. Testing sign intervals around the critical points x=-3 (excluded) and x=4 shows the expression is negative or zero exactly when -3 < x <= 4.
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.