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Objective- To recognize symbols, variables, and types of sentences used in algebra. Equalities = Equals- is the same as Congruent- same size and shape ~ Similar- same shape Inequalities < Is less than > Is greater than Is less than or equal to Approx. equal to = Not equal to Expressions vs. Equations Sentences Expressions Numerical Variable 2+3 5(8) - 4 x+7 8 - 3y Equations 2+3=5 4 + 2(3) = 10 x - 4 = 13 11= 3 + 2m Inequalities 9-5>3 6y - 4 < 8 Open sentences Open sentences have solutions and can be solved. Identify each as an expression, sentence, open sentence, equation, or inequality. 1) 3x + 5 = 11 Sentence, open sentence, equation 2) 7 < 2(5) + 3 Sentence, inequality 3) 5x - 2 Expression 4) 6m + 2 > 3 Sentence, open sentence, inequality Open sentences have solutions and can be solved. Variable Equations 4+m=7 -4 -4 m=3 One Solution Variable Inequalities 5 + y < 91 -5 -5 y < 86 Infinite Solutions Use mental math to solve each equation. 1) x + 4 = 9 {5} 2) 5 - x = 2 {3} 3) 2x + 3 = 17 {7} 4) x x 0 { 0, 1 } 2 Give three solutions to each sentence below. 1) x > 10 Samples: 11, 15, 34 2) x + 3 7 Samples: 4, -8, 0 3) 5 - x < 0 Samples: 6, 7, 10 4) 2x 1 3 Samples: 3, 4, 7