Question

Which inequality has a solution set of {x ⎸x > 3 or x < –3}? Question 16 options: a) |2| < 6 b) |2| ≥ 6 c) |2| > 6 d) |2| ≤ 6

Answer 1

Option C) |2x| > 6 is correct.

Explanation:

Consider the provided solution set:

{x ⎸x > 3 or x < –3}

Now check which options are correct.

Option A) |2x| < 6

`\mathrm{If}\:|u|\:<\:a,\:a>0\:\mathrm{then}\:-a\:<\:u\:<\:a`

`-6<2x<6`

`-3<x<3`

Thus, the option is incorrect.

Option B) |2x| ≥ 6

`\mathrm{If}\:|u|\:\ge \:a,\:a\:>\:0\:\mathrm{then}\:u\:\le \:-a\:\quad \mathrm{or}\quad \:u\:\ge \:a`

`2x\le \:-6\quad \mathrm{or}\quad \:2x\ge \:6`

`2x\le \:-6\quad \mathrm{or}\quad \:2x\ge \:6`

Thus, the option is incorrect.

Option C) |2x| > 6

`\mathrm{If}\:|u|\:>\:a,\:a>0\:\mathrm{then}\:u\:<\:-a\:\quad \mathrm{or}\quad \:u\:>\:a`

`2x<-6\quad \mathrm{or}\quad \:2x>6`

`x<-3\quad \mathrm{or}\quad \:x>3`

Thus, the option is correct.

Option C) |2x| ≤ 6

`\mathrm{If}\:|u|\:\le \:a,\:a\:>\:0\:\mathrm{then}\:-a\:\le \:u\:\le \:a`

`2x\ge \:-6\quad \mathrm{and}\quad \:2x\le \:6`

`x\ge \:-3\quad \mathrm{and}\quad \:x\le \:3`

Thus, the option is incorrect.

Hence, Option C) |2x| > 6 is correct.