Objective - To solve equations over given replacement sets.

1. Objective - To solve equations over given replacement sets. Inequalities Equalities < 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. State whether each sentence is true, false ,or open. 1) 8 + 5 = 13 5) 14 - 2(3) = 8 True True 2) 2x - 1 = 9 6) 9 = 7 + 4y Open Open 3) 17 = 3(5) + 1 7) 13 - 2 = 9 False False 4) 3 = 7(2) - 5 8) t + t = 5(2) + 1 False Open

5. Replacement Set Equation Solution Set Try each key:

6. Solve the given equation using the replacement set {0, 1, 2, 3, 4}. 1) 6 - x = 2 5) 2x = x + x {4} {0, 1, 2, 3, 4} 2) 2x + 1 = 5 6) 9 = 7 + 2y {2} {1} 3) 5x = 15 7) x + 5 = 27 { } {3} , or “No solution” 4) 11 = 4x + 3 8) x + 2 = x { } {2} , or “No solution”

7. Equivalent Equations Addition Property of Equality If a = b, then a + c = b + c or Given a = b and c = c then a + c = b + c Subtraction Property of Equality If a = b, then a - c = b - c or Given a = b and c = c then a - c = b - c

8. x + 3 = 7 Heavier - 3

9. x = 7 Heavier

10. x = 7 Heavier

11. x = 7 Heavier

12. x = Heavier 7

13. - 3 - 3 x = 4 x + 3 = 7 Algebraically, x + 3 = 7 x + 3 = 7 -3 -3 x + 3 - 3 = 7 - 3 x = 4 x = 4

14. Rules for Transforming Equations 1) Goal: Isolate the variable on one side of the equation. 2) Always perform the same operation to both sides of an equation. 3) To undo an operation, perform its opposite operation to both sides of the equation.

15. Solve the equations below. The replacement set is the set of whole numbers. 1) x + 3 = 10 4) 13 = x + 5 - 3 - 3 - 5 - 5 x = 7 8 = x 2) y - 8 = 11 5) 12 = n - 3 +8 +8 +3 +3 y = 19 15 = n 3) n + 5 = 11 6) 11 + 3 = k - 5 - 5 14 = k n = 6

16. Translate the sentence into an equation and solve. 1) The sum of k and 13 is 28. k + 13 = 28 - 13 - 13 k = 15 2) Five is the difference of t and 4. 5 = t - 4 +4 +4 9 = t

17. If a = b, then a c = b c. Multiplication Property of Equality or

18. Solve given the replacement set is the set of whole numbers. 1) 3) 2) 4)

19. Division Property of Equality or

20. Solve given the replacement set is the set of whole numbers. 1) 3) 2) 4) No solution

21. Each pair of equations is equivalent. Tell what was done to the first equation to get the second. Four was subtracted from both sides. Nine was added to both sides. Each side was multiplied by 4.

22. Each pair of equations is equivalent. Tell what was done to the first equation to get the second. Each side was divided by 6. Six was subtracted from both sides. Each side was multiplied by 7.