SAT Mathematics Practice Test 4

Adding 4 to each side of the inequality $3\mathit{p}-2\ge 1$ yields the inequality $3\mathit{p}+2\ge 5$. Therefore, the least possible value of $3\mathit{p}+2$ is 5.
Choice B is incorrect because it gives the least possible value of $3\mathit{p}$, not of $3\mathit{p}+2.$ Choice C is incorrect. If the least possible value of $3\mathit{p}+2$ were 2, then it would follow that $3\mathit{p}+2\ge 2$. Subtracting 4 from each side of this in equality would yield $3\mathit{p}-2\ge -2$. This contradicts the given inequality, $3\mathit{p}-2\ge 1$.Therefore, the least possible value of $3\mathit{p}+2$ cannot be 2. Choice D is incorrect because it gives the least possible value of p, not of $3\mathit{p}+2$.