SAT Linear inequalities in one or two variables Practice Question 19 (Hard)

Question bank / Linear inequalities in one or two variables

Math · AlgebraHard

In the inequality $kx + 3 > 2x - 5$ , $k$ is a constant. For which value of $k$ is the inequality true for all real values of $x$ ?

$-2$

$0$

$2$

$8$

Show answer and explanation

Answer: C

Rearrange: $(k - 2)x > -8$ . If $k - 2 \ne 0$ , the inequality fails for some $x$ (large positive or large negative values). If $k = 2$ , it becomes $0 > -8$ , which is true for every $x$ . So $k = 2$ .

Choice D might come from setting $k$ equal to the gap between the constants, but with $k = 8$ the inequality fails for $x \le -\frac{4}{3}$ .

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