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