If \(x\) is an integer, what is the solution set of \(3x+2\ge -4\) and \(x<5\)?

Correct answer: \(x\in\{-2,-1,0,1,2,3,4\}\)

Solve each inequality separately and then take their intersection. From \(3x+2\ge -4\), subtracting 2 gives \(3x\ge -6\), so division by the positive number 3 gives \(x\ge -2\). The second condition is \(x<5\). Hence, over the real numbers, the combined interval is \([-2,5)\). Since the question restricts \(x\) to integers, the permitted values are \(-2,-1,0,1,2,3,4\). Thus option A is correct. Option B omits -2 and includes 5, option C incorrectly includes 5, and option D starts below the lower bound and misses 4. The strict sign at 5 excludes that endpoint.