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Lesson 3.5 Compound Inequalities
Read pages 161 – 163
Definition:
Compound Inequality: Two inequalities that are joined by the word and or the word or
Compound inequalities in math are just like compound sentences in English. Compound
sentences in English can be combined with the words and/or. For example if we take
these two sentences and combine them into one sentence: Jane went to the grocery store.
Jane also went to the mall. We can combine those two sentences into one sentence using
the word and. Jane went to the grocery store and the mall.
And: When both situations must happen
Or: When only one of the two situations must happen at a time
Example 1: Using and to Combine Inequalities
Age
Since the variable is in the middle of the inequalities we will use the word and to separate
them.
 4  r  5  1
4  r 5
1 r
and
r  5  1
r4
Example 2: Using or to Combine Inequalities
Solve the combine inequality: 4v  3  5 or  2v  7  1
4v  3  5
4v  8
 2v  7  1
OR
v  2
 2v  6
v3
Writing and Graphing Compound Inequalities
a. all real numbers that are at least -2 and at most 4
2 x  4
b. Today’s temperatures will be above 32 but not as high as 40
32  x  40
c. all real numbers that are less than -3 or greater than 7
x  3 OR x  7
Check for Understanding:
Solve each inequality.
1.  3  j  2  7
2. 3b  1  7 OR 4b  1  9
For each situation write and graph an inequality.
3. all real numbers n that are at most -3 or at least 5
4. all real numbers that are between -4 and 6
Homework: Pages 163 – 164 #s 1 – 4 all; 6 – 18 evens; 20 – 23 all; 24 – 32 evens