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Combined Inequalities. Compound Inequalities. In mathematics the words AND and OR have very precise meanings. When we put together two or more inequalities we should pay special attention to which word is used. Consider the following statements:

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## Combined Inequalities

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**Compound Inequalities**• In mathematics the words AND and OR have very precise meanings. When we put together two or more inequalities we should pay special attention to which word is used. • Consider the following statements: • “Water which is kept at a temperature above 212º below 32 º will not remain liquid.” • “Cars on the interstate must maintain a speed above 45 mph below 75 mph.” OR AND**Conjunction (and)**• A conjunction is a sentence formed by joining two sentences with the word and. The solution is the area in common.**20 21 22 23 24 25 26 27 28**20 21 22 23 24 25 26 27 28 20 21 22 23 24 25 26 27 28 The Solution set is: {23,25 and all real number between 23 & 25.}**20 21 22 23 24 25 26 27 28**20 21 22 23 24 25 26 27 28 20 21 22 23 24 25 26 27 28 No Solution!!**Disjunction (or)**• A disjunction is a sentence formed by joining two sentences with the word or. The solution is the area of both sentences.**-2 -1 0 1 2 3 4 5**6 -2 -1 0 1 2 3 4 5 6 -2 -1 0 1 2 3 4 5 6**-2 -1 0 1 2 3 4 5**6 -2 -1 0 1 2 3 4 5 6 -2 -1 0 1 2 3 4 5 6**-2 -1 0 1 2 3 4 5**6 -2 -1 0 1 2 3 4 5 6 -2 -1 0 1 2 3 4 5 6 The solution set is: {all real numbers}.**Graph the following inequality.**Your Turn x < -4 or x> 5 TRY THIS -4 5

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