# Inequalities vs Equations

- Author:
- Patrick Hashem, Kevin Hopkins

- Topic:
- Algebra, Equations, Inequalities

## Math Sentences

Consider the following math sentence and find the answer(s).

## x+5=8

How many answers did you find for this math sentence? What is the answer(s)? (what value of the variable x would make the equation true?)

## Explain your answer!

What steps did you take to find the answer ?

## Different Math Sentences

Describe the difference between the following two math sentences: and

## A New Type of Math Sentence: Inequalities

An

*equation*is a type of math sentence where either side of the*equals*sign must have the exact same value. An*inequality*is a type of math sentence where either side of the*inequality symbol (greater than, less than, greater than or equal to, less than or equal to)*. The equations we have seen only have*one answer*. The inequalities we will work with will have*infinite answers.*We solve inequalities the same way we solve equations, using opposite operations.## Inequality Symbols

__Greater than: (>)__x is greater than 5

__Less than: (<)__7 is less than 10

__Greater than or equal to: (__

__)__10 is greater than or equal to 10

__Less than or equal to: (__

__)__x is less than or equal to 3

## Identifying possible answers

List 4 numbers that make the following inequalities true. (x is greater than 5) (x is less than or equal to 8)

## NOTICE!

Is there any limit to the number of answers we can come up with?
Inequalities will have an infinite number of solutions where equations will normally only have one solution