2. An inequality is a mathematical sentence that contains the following symbols: .
< , >,
is less than or equal to
is greater than or equal to
is less than
is greater than
<
>
A solution to an inequality is any number that makes it true.
Inequalities have many solutions.
Solutions are shown by shading a number line.

3. Graph each inequality solution on a number line:
The open circle means the 1 is not included in the solution. A.
x < 1
The solution is all numbers less than 1.
The closed circle means the −2 is included in the solution. B.
The solution is all numbers greater than or equal to −2.

4. Solve this inequality and graph the solution. x + 5 < 7 − 5 − 5
To solve an inequality, follow the same steps you use to solve an equation.
Solve this inequality and graph the solution.
x < 7
− 5
− 5
Graph:
x < 2
The solution is all numbers less than 2.
Check:
Try 1, a number less than 2. x 1
+ 5 < 7
6 < 7
This sentence is true.

5. Solve this inequality and graph the solution.
x − − 5
Graph:
x −2
The solution is all numbers greater than or equal to −2.
Check:
Try −1, a number greater than −2. −1 x
− −5
−1 + (−3) −5
− −5
This sentence is true.

6. Solve these inequalities and graph the solution.
Try These:
Solve these inequalities and graph the solution.
x −2 −1 −1
Graph:
x −3
x – 7 > – 5
Graph:
+ 7
+ 7
x > 2

7. Solve these inequalities and graph the solution.
3 x ≥ 9
Graph:
x ≥ 3
< 3
Graph:
( 2 ) .
< 3
. ( 2 )
x < 6

8. Solve this inequality and graph the solution.
4 n > 16
n > 4
Graph:

9. Solve this inequality and graph the solution.
2x − 8 > −10
2x > −2 2 2
x > −1
Graph:

10. Write an inequality for each sentence.
In Florida you can vote if you are at least 18 years old. Write an inequality showing the age of all voters in Florida.
( Let x = the voter’s age) x
You must be less than 16 years old to play on a certain youth baseball team. Write an inequality showing the age of the players.
( Let n = the player’ s age)
n < 16

11. Write an inequality for each sentence and solve it.
Four times a number is less than 12.
4 n < 12
Graph: 4 4
n < 3
The sum of a number and 2 is at least 4. n
Graph: −2 −2 n

12. Use an inequality to solve problems.
A pair of jeans costs $25 and a shirt costs $10. You have $50 to spend. Write an inequality to find how many shirts you can buy along with one pair of jeans.
( Let n = the number of shirts)
10n ≤ 50
−25
−25
10n ≤ 25 10 10
n ≤ 2.5
You can buy 2 shirts.