Question

The inequality |3-4| > 3 is equivalent to O (A) -3 7 O (D) x < -1 or 2 >7 O (E) r < 1 or r > 7​

Answer 1

Answer: Choice (E) x < 1 or x > 7

=========================================================

Step-by-step explanation:

Rule: if |x| > k, then x < -k or x > k

Using that rule for the given inequality means we have these steps

|x-4| > 3

x-4 < -3 or x-4 > 3

x < -3+4 or x > 3+4

x < 1 or x > 7 ..... choice E

-------------

Here's a visual way to see why this is the case.

|x-4| represents the distance from x to 4 on the number line.

When we say |x-4| > 3, we want to know which points are more than 3 units away from 4 on the number line.

We can plot 4 on the number line, and then measure 3 units below it (to get to 1) and then 3 units above it (to get to 7). If we're in the region 1 < x < 7, then we're within 3 units of 4 on the number line. Otherwise, we're more than 3 units away from the target we're after.