Which is the solution set of 7x + 2 ≥ 3x − 18?

Correct answer: {x : x ≥ −5}

The governing concept is solving a linear inequality and expressing its answer in set-builder notation. Begin with 7x + 2 ≥ 3x − 18. Subtract 3x from both sides to obtain 4x + 2 ≥ −18. Then subtract 2, giving 4x ≥ −20. Dividing by the positive number 4 preserves the inequality sign, so x ≥ −5. In set notation, the solution is {x : x ≥ −5}, which includes −5 because equality is permitted by the original ≥ sign. Therefore option D is correct. Option A reverses the direction, option B incorrectly excludes the endpoint, and option C uses the wrong strict direction. A useful check is x = −5: both sides become −33, so equality holds and −5 must be included.