Objective- To recognize symbols, variables, and types of sentences used in algebra.

1. Inequalities Equalities Objective- To recognize symbols, variables, and types of sentences used in algebra. < 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 =

2. 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.

3. 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

4. Open sentences have solutions and can be solved. Variable Equations Variable Inequalities 4 + m = 7 5 + y < 91 - 4 - 4 - 5 - 5 m = 3 y < 86 Infinite Solutions One Solution

5. Give three solutions to each sentence below. Samples: 11, 15, 34 1) x > 10 2) x + 3 7 Samples: 4, -8, 0 Samples: 6, 7, 10 3) 5 - x < 0 4) Samples: 3, 4, 7

6. Objective - To translate English words, phrases, and sentences into mathematical symbols, expressions, and equations respectively. _ + minus times divide plus subtract multiply quotient add decreased by product increased by diminished by …of... sum difference twice ( 2) total less more than less than subtracted from

7. Tricky Ones! 5 plus x 5 + x 5 + x add 5 and 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

8. Tricky Ones! 5 minus x 5 - x 5 - x 5 less 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

9. 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

10. 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)

11. 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