Question

What is the solution of |x – 2| > –3? Explain.

Answer 1

This question literally translates to the following:

For what values of x is |x - 2| greater than -3?

Think about it a little. The question is not as hard as you think.

Answer 2

remember that | | makes what's inside a positive number.

in other words | stuff | is ALWAYS 0 or bigger.

Answer 3

Note: When you use the absolute bars, the lowest value it can have is zero. It is always positive or zero and never negative.

Answer 4

@phi Looks like we have all kinds of Greek letters in here, eh?

Answer 5

in other words, for any value of x, you will get a number 0 or bigger.

is 0 (or bigger) bigger than -3 ?

Answer 6

x> -1 maybe?
Or does this have two answers? Like, x<5 as well?

Answer 7

The left hand side of the inequality has absolute bars. That means, no matter what x is, the left hand side will ALWAYS be greater than or equal to zero. The right hand side is negative. Therefore, LHS will always be greater than RHS no matter what x is. The answer is all real numbers for x will satisfy this inequality.

Answer 8

Okay so x> -1 or x>5?

Answer 9

Right?

Answer 10

No. ALL values of x satisfies that inequality. x can be ANY negative number, zero or ANY positive number and it will satisfy that inequality. The answer is x can be ANY real number.

Answer 11

I'm confused. It says to solve and I thought you did it just like a regular inequality. Can you walk me throughout the problem because I have no idea what to do.

Answer 12

When you come across an inequality |a| > b it usually splits into two parts:
a > b or a < -b

Here, |x – 2| > –3.
Therefore, x-2 > -3 OR x-2 < 3
x > -1 OR x < 5
Pick any x value and it will ALWAYS satisfy either the first one OR the second one. Therefore, the solution is ALL values of x.

If the inequality were split into two parts that says: x > -1 AND x < 5 then x will be limited to values between -1 and +5. But with ">" or ">=" inequalities it is OR not AND. So any value of x will satisfy the above set of two inequalities: x > -1 OR x < 5

Answer 13

Okay. Thanks so much. I had that originally but didn't know how to word it and then confused myself into oblivion so thanks again!

Answer 14

You are welcome.

If the original inequality was |x – 2| > +3 (that is, plus 3 instead of -3) then:
x - 2 > 3 OR x - 2 < -3
x > 5 OR x < -1

Here the solution will be: x: (-infinity, -1) U (5, +infinity).

But with minus 3 on the RHS all x values will satisfy the inequality.