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{ , 3, 2, 1, 0, 1, 2, 3, }ExerciseUse ellipses and set notation to list the set of all integers.1x, x + 1, x + 2Use algebraic expressions to represent three consecutive integers.Exercise2x, x + 2, x + 4Use algebraic expressions to represent three consecutive odd integers.Exercise3I = the number of Emilys lamps; (I 4) + I > 20Ann has four fewer lamps than Emily, and together they have more than 20 lamps. What is the minimum number of lamps Emily could own?Exercise4h = the number of hot dogs; 2.45 + 1.25h 6Larry wants to spend no more than $6 for lunch. If he has already purchased a drink and tater tots for $2.45, how many hot dogs can he purchase if they cost $1.25?Exercise5Mr. Tobin must spend less than $62.50 per tire.Mr. Tobin wants to buy four new tires and spend less than $250. What is the range of prices he can spend per tire?Let n = cost per tire.4n < 25044n < 62.50Example 16Consecutive Integersintegers: n, n + 1, n + 2, etc.even integers: n, n + 2, n + 4, etc.odd integers: n, n + 2, n + 4, etc.The sum of three consecutive integers is more than 20. What are the smallest possible values for the integers?Let n = the first integer.Let n + 1 = the second integer.Let n + 2 = the third integer.Example 2833n + (n + 1) + (n + 2) > 203n + 3 > 203n + 3 3 > 20 33n > 17n > 5239The smallest possible integer value for n is 6. The three consecutive integers are 6, 7, and 8. Check: 6 + 7 + 8 > 2021 > 2010Four times the smaller of two consecutive odd integers is less than three times the larger. What are the largest possible values for the integers?Let n = the first odd integer.Let n + 2 = the second odd integer.Example 3114n < 3(n + 2)4n < 3n + 64n 3n < 3n 3n + 6 n < 6 The largest odd integer for n is 5. The second integer would be 5 + 2 = 7.Check: 4(5) < 3(7)20 < 2112Trichotomy AxiomFor all real numbers a and b, a > b, a < b, or a = b.less than, equal to, greater than

x < 3Solve 5x + 7 22. 5x + 7 > 22 5x > 15 5 5 5x + 7 7 > 22 7Example 4Common WordingNegatedMeaningEquivalentis at most or is not more than or is the maximum amount>is less than or equal toCommon WordingNegatedMeaningEquivalentis at least or is not less than or is the minimum amount