Name: ______________________
Class: __________________
AU1: Notes #8 – Inequalities
Date: __________________
Vocabulary:
Inequality is a mathematical sentence that compares two unequal expressions.
Here is a chart of words or phrases associated with the inequality symbols:




Open dot means the number is __________ of the solution set, thus it is not shaded.
Closed dot means the number ____________ of the solution set, thus it is shaded.
Problem Solving Tip
Notice that anytime that you can say “equal to” the dot is closed.
Otherwise the dot is open.
Therefore: the open dots are < and > and .
The closed dots are
and =.
1
Example 1: Translate and graph the solution set for the following sentences:
A number q is less than 2.
Example 2: Given the following inequality, write a word sentence and graph the inequality.
x  4
Example 3: Given the following graph, write the inequality and a word sentence.
2
Try-It!: Given the word sentence, inequality, or graph write the other two representations.
1. y is less than negative four
2. k is no more than seven.
3. p has a minimum of negative five.
4. the temperature in a refrigerated truck must be kept at or below 38oF.
5. at least twenty students were sick with the flu.
3
6. x  0
7. x 
1
2
8. 2  x
9.  5  b
10.
11.
12.
4
Solving Inequalities
You can solve inequalities the same way that you solve equations by using inverse
operations. The only difference is that you are not finding one solution for the variable; you are
finding infinitely many solutions. Hence the reason you graph the solution on the number line.
Example 1:
Two less than three times a number x is less than or equal to negative fourteen.
Try-It! Solve and graph the solution set.
3  4d  7
5
Example 2:
So far you have not run into any problems with regard to solving inequalities and graphing them.
The inverse operation has worked thus far, however when you divide or multiply by a negative
number it will require a little more work to get to the appropriate answer.
Solve and graph the solution set for the following problems.
A.
−2x > 6
B.
1
 n5
2
6
Try-It! Solve and graph the solution set.
A.
 4 p  28  8
B.
2h  13  23
7
Practice: Solve and graph the following inequalities, make your own number line.
1.
 5m  20
2.
j
0
6
3.
5a  10
4.
c
6
3
5.
m6  2
6.
y  3  4
7.
4x  11  19
8.
6
9.
27  0.9r
10.
5m  3  18
Write an inequality for the graph.
11.
12.
8
x
2