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Writing Inequalities
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2. ≥ : greater than or equal to
An inequality is like an equation, but instead of an equal sign (=) it has one of these signs:
< : less than
≤ : less than or equal to
> : greater than
≥ : greater than or equal to

3. What do Inequalities mean?
A mathematical sentence that uses one of the inequality symbols to state the relationship between two quantities.

4. Mathematics is not always about "equals"
Mathematics is not always about "equals"! Sometimes we only know that something is bigger or smaller than something else.

5. Example: Alex and Billy have a race, and Billy wins!
What do we know?
We don't know how fast they ran, but we do know that Billy was faster than Alex:
Billy was faster than Alex
We can write that down like this:
b > a
(Where "b" means how fast Billy was, ">" means "greater than", and "a" means how fast Alex was)

6. Example: Alex plays in the under 15yr soccer. How old is Alex?
We don't know exactly how old Alex is, because it doesn't say "equals"
But we do know "less than 15", so we can write:
a < 15
The small end points to "a" because the age is smaller than 15.

7. Example: you must be 13 or older to watch a movie.
The "inequality" is between your age and the age of 13.
Your age must be "greater than or equal to 13", which is written:
Age ≥ 13

8. Graphing Inequalities
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Graphing Inequalities
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9. Graphing Inequalities
When we graph an inequality on a number line we use open and closed circles to represent the number.
Plot an open circle
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< ≤ ≥
Plot a closed circle

10. x < 5 means that whatever value x has, it must be less than 5.
Try to name ten numbers that are less than 5!

11. Numbers less than 5 are to the left of 5 on the number line.5 10 15
-20
-15
-10 -5
-25 20 25
If you said 4, 3, 2, 1, 0, -1, -2, -3, etc., you are right.
There are also numbers in between the integers, like 2.5, 1/2, -7.9, etc.
The number 5 would not be a correct answer, though, because 5 is not less than 5.

12. Try to name ten numbers that are greater than or equal to
x ≥ -2
means that whatever value x has, it must be greater than or equal to -2.
Try to name ten numbers that are greater than or equal to -2

13. Numbers greater than -2 are to the right of -2 on the number line.5 10 15
-20
-15
-10 -5
-25 20 25 -2
If you said -1, 0, 1, 2, 3, 4, 5, etc., you are right.
There are also numbers in between the integers, like -1/2, 0.2, 3.1, 5.5, etc.
The number -2 would also be a correct answer, because of the phrase, “or equal to”.

14. Solving Inequalities

15. Solving an Inequality The goal is to get the variable by itself.
Follow the same rules and steps that we used to solve an equation. USE OPPOSITE OPERATIONS TO UNDO.
1. Always undo addition or subtraction first, then multiplication or division
Remember whatever is done to one side of the inequality must be done to the other side.

16. Solve an Inequality w + 5 < 8 - 5 -5 w < 3
w < 3
All numbers less than 3 are solutions to this problem! 5 10 15
-20
-15
-10 -5
-25 20 25

17. More Examples
8 + r ≥ 12
r 4
All numbers greater than 4 (including 4) ≥ 5 10 15
-20
-15
-10 -5
-25 20 25

18. All numbers less than 8 (including 8)
More Examples
2h + 8 ≤ 24
2h ≤ 16
h ≤ 8
All numbers less than 8 (including 8) 5 10 15
-20
-15
-10 -5
-25 20 25

19. More Examples 2x > 2 2 2 x > 1
x > 1
All numbers greater than 1 make this problem true! 5 10 15
-20
-15
-10 -5
-25 20 25

20. Your Turn…. x > 1 d > 4 x < 11 c < 3 x + 3 > 4
Solve the inequality and graph the answer.
x + 3 > 4
6d > 24
2x - 8 < 14
2c – 4 < 2