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 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 Objective - To translate English words, phrases, and sentences into mathematical symbols, expressions, and equations respectively. _ + minus times divide plus subtract multiply quotient add increased by decreased by product diminished by …of... sum difference twice ( 2) total less more than less than subtracted from Tricky Ones! 5 plus x 5+x add 5 and x 5+x the sum of 5 and x 5+x 5 increased by x 5+x 5 more than x x+5 5 is more than x 5>x Tricky Ones! 5 minus x 5-x 5 less x 5-x the difference of 5 and x 5-x 5 decreased by x 5-x 5 less than x x-5 5 subtracted from x x-5 5 is less than x 5<x Translate each phrase into a mathematical expression. 1) 5 subtract x 5-x 2) the product of 10 and y 10y 3) 20 decreased by a number t 20 - t 4) 6 added to the product of 11 and m 5) the quotient of y and 9 6) 8 less than 7 times k y 7k - 8 9 11m + 6 Translate each phrase into a mathematical expression. 1) six less than twice a number x 2x - 6 2) five times the sum of y and 4 5(y + 4) 3) twice the difference of m and 3 2(m - 3) 4) the quotient of 7 and a number x less 2 7 x-2 5) the difference of 6 and k divided by 9 (6 - k) 9 6) 4 times the sum of 12 and y 4(12 + y) Translate each sentence into a mathematical equation or inequality. 1) Eight less than twice the sum of four and y is the same as 19. 2(4 + y) - 8 = 19 2) Six more than x is more than twice the difference of x and 7. x + 6 > 2(x - 7) 3) The quotient of m and 3 is six less than the product of 10 and m. m 3 = 10m - 6 4) Five less than x is less than five less x. x-5<5-x