SAT Math · Linear inequalities in one or two variables · medium

What is the solution set of the system x > -3, x ≤ 5, and 2x - 1 < 9?

What is the solution set of the system x>−3x > -3, x≤5x \leq 5, and 2x−1<92x - 1 < 9?

Answer and explanation

Answer: B: -3 < x < 5

Solve the third inequality first: 2x−1<92x - 1 < 9 gives 2x<102x < 10, so x<5x < 5. All three conditions must hold at once: x>−3x > -3, x≤5x \leq 5, and x<5x < 5. The upper limits x≤5x \leq 5 and x<5x < 5 overlap, and the stricter one wins, since x=5x = 5 fails x<5x < 5. The solution is −3<x<5-3 < x < 5, choice B. Choice A keeps x≤5x \leq 5, which wrongly allows x=5x = 5. Choice C (x<5x < 5) drops the lower bound. Choice D uses 9, which is the right side of the third inequality before solving, an unfinished step.

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