Objective- To translate words and phrases into symbols, variables, expressions and equations Equalities Inequalities < Is less than = Equals- Is the same as > Is greater than Congruent- same size and shape Is less than or equal to ~ Approx. equal to Similar- same shape = Not equal to

Expressions vs. Equations Sentences Expressions Equations Inequalities 2 + 3 2 + 3 = 5 9 - 5 > 3 Numerical 5(8) - 4 4 + 2(3) = 10 x + 7 x - 4 = 13 Variable 6y - 4 < 8 8 - 3y 11= 3 + 2m 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 open sentence, equation 2) 7 < 2(5) + 3 Sentence, inequality (nothing to solve) 3) 5x - 2 Expression (can’t be solved) 4) 6m + 2 > 3 open sentence, inequality

_ Operations and common phrases + plus minus times divide add subtract multiply quotient increased by decreased by product sum diminished by twice ( 2) total difference …of... less more than less than subtracted from

Translates to the expression the sum of 5 and x Addition 5 plus x add 5 and x 5 + x 5 increased by x Translates to the expression x + 5 5 more than x 5 > x 5 is more than x

Translates to the expression Subtraction the difference of 5 and x 5 minus x 5 - x 5 less x Translates to the expression 5 decreased by x x - 5 5 less than x 5 < x 5 subtracted from x 5 is less than x

3) 20 decreased by a number t 4) 6 added to the product of 11 and m Translate each phrase into a mathematical expression. 1) 5 subtract x 2) the product of 10 and y 3) 20 decreased by a number 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 5 - x 10y 20 - t 11m + 6 y 9 7k - 8

1) six less than twice a number x 2) five times the sum of y and 4 Translate each phrase into a mathematical expression. 1) six less than twice a number x 2) five times the sum of y and 4 3) twice the difference of m and 3 4) the quotient of 7 and a number x less 2 5) the difference of 6 and k divided by 9 6) 4 times the sum of 12 and y 2x - 6 5(y + 4) 2(m - 3) 7 x - 2 (6 - k) 9 4(12 + y)

1) Eight less than twice the sum of four and y is the same as 19. 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) Six more than x is more than twice the difference of x and 7. 3) The quotient of m and 3 is six less than the product of 10 and m. 4) Five less than x is less than five less x. 2(4 + y) - 8 = 19 x + 6 > 2(x - 7) m 3 = 10m - 6 x - 5 < 5 - x