Question

What is the solution to the inequality |X-4|<3?

Answer 1

Answer:

1 < x < 7

Step-by-step explanation:

When you see an absolute value expression in an equation or inequality, you need to split it into two to solve algebraically for some unknown x.

This can can be broken into x - 4 < 3 and -(x - 4) < 3. (Basically, the logic behind this is that |x - 4| < 3 means that (x - 4)'s distance from 0 has to be less than 3, which means that both (x - 4) and -(x - 4) need to be less than 3.)

Let's start with the first one.

x - 4 < 3

Just add 4 to both sides, and you have x < 7. Easy.

Second one.

-(x-4) < 3

-x + 4 < 3

Add x to both sides.

4 < x + 3

Keep solving; subtract 3 from both sides.

1 < x

So you have x < 7 from the first one and x > 1 from the second one, which gives you 1 < x < 7!