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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 r4 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 v3 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