I am very confused on how to find the absolute value of an equation without graphing it first. Can you help me?

Tutors, sign in to answer this question.

The definition of absolute value is |x| = { x if x >=0; or -x if x < 0 }.

Note that sqrt(x^2) = |x|.

E.g., if y = x^2 - 1, find |y|.

Case 1: If x^2 - 1 < 0, or x^2 < 1, or sqrt(x^2) < sqrt(1), or |x| < 1, or -1 < x < 1,

then |y| = -y = 1 - x^2.

Case 2: If x^2 - 1 >= 0, or x <= -1 or x >= 1,

then |y| = +y = x^2 - 1.

|y| is a piecewise function: |y| = { 1 - x^2 if -1 < x < 1; or x^2 -1 otherwise }.

Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...

l Q I = - Q for Q <0

Example : Evaluate the following expression for 5 < X < 9

l l X - 14 l - l x - 3 l l =

l - X +14 + X - 3 l = l 14-3 l = l 11l = 11

Note that l x- 14l = - x + 14 for 5< X<9

l X - 3 l = X -3 for 5 <X< 9

Dear Jaws,

Let's take an example:

Suppose you are given this inequality regarding absolute value

⌈x – 1⌉ < 3

All you have to do to get rid of the absolute value notation is to rewrite the expression as

-3 < (x - 1) < 3

Add 1 to each side to get

-2 < x < 4

It doesn't make any difference if you are dealing with =, <, >, ≤ or ≥, the idea is the same.

In general terms, if f(x) is some function of x

⌈f(x)⌉ =, or <, or >, or ≤, or ≥ n, then

-n =, or <, or >, or ≤, or ≥ f(x) =, or <, or >, or ≤, or ≥ n

Already have an account? Log in

By signing up, I agree to Wyzant’s terms of use and privacy policy.

Or

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Your Facebook email address is associated with a Wyzant tutor account. Please use a different email address to create a new student account.

Good news! It looks like you already have an account registered with the email address **you provided**.

It looks like this is your first time here. Welcome!

To present the tutors that are the best fit for you, we’ll need your ZIP code.

Please try again, our system had a problem processing your request.

## Comments