ShmoopTube

00:09

Equations come in all different shapes and sizes,

00:11

no matter how much they try sticking to their diets.

00:16

Some equations have no solutions.

00:18

These are called contradictions.

00:21

No they're not. Yes, they are.

00:25

For instance, the equation X + 1 = X + 5

00:29

would be a contradiction

00:31

because no value of X will make that equation true.

00:36

It would be like saying a zebra is the same thing as a lion.

00:42

There can also be equations with infinite solutions, which are called identities.

00:47

Anything you plug into these equations will make the equation true.

00:50

The equation 2 X + 1 = 2X + 1 is an identity

00:54

because it'll always be true for any value of X.

00:58

It's like a mirror. Anything placed in front of the mirror will be reflected back.

01:04

Conditional equations have a limited number of solutions.

01:08

These guys are only true when certain values are plugged in.

01:11

The equation 2X = 6 is limited

01:13

because it'll only work when X is 3.

01:16

No other value will make the equation true.

01:23

It'd be like saying only zebras are acceptable for tourists, and no other animals.

01:28

The important thing is to find out what type of equation you're facing.

01:32

Otherwise, you might get into some trouble.

Full Transcript