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

Which of the following is equivalent to -3x + 5 ≤ 20?

Which of the following is equivalent to −3x+5≤20-3x + 5 \leq 20?

Answer and explanation

Answer: B: x ≥ -5

Subtract 5 from both sides of −3x+5≤20-3x + 5 \leq 20: −3x≤15-3x \leq 15. Divide both sides by −3-3 and reverse the inequality: x≥−5x \geq -5, choice B. Test x=0x = 0: 5≤205 \leq 20 is true, and 0≥−50 \geq -5 is true. Choice A (x≤−5x \leq -5) forgets to reverse the inequality. Choice C (x≥5x \geq 5) reverses the sign but loses the negative on the 5. Choice D (x≤5x \leq 5) drops both the sign flip and the negative. Whenever you divide or multiply by a negative number, flip the direction of the inequality.

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