Which of the following is equivalent to the pair of inequalities \(x + 6 > 10\) and \(x - 3 \le 5 ?\)

M7MBA wrote: ↑

Sat Jun 05, 2021 5:18 am

Which of the following is equivalent to the pair of inequalities \(x + 6 > 10\) and \(x - 3 \le 5 ?\)

(A) \(2 < x < 16\)
(B) \(2 \le x < 4\)
(C) \(2 < x \le 8\)
(D) \(4 < x \le 8\)
(E) \(4 \le x \le 16\)

Answer: D

Source: Official Guide

When it comes to multiple inequalities, I find that it helps to rearrange them so that the inequality signs are all facing the same direction (I prefer arranging them so that the values are in ascending order from left to right)

So, x + 6 > 10 and x - 3 < 5 first become 10 < x + 6 and x - 3 < 5
For 10 < x + 6, we subtract 6 from both sides to get: 4 < x
For x - 3 < 5, we add 3 to both sides to get: x < 8
With the two inequality signs facing the same direction, it's easy to combine them to get 4 < x < 8