Jag Nation Pride

1. Jag Nation Pride When you enter this classroom, immediately do the following: • Take your seat. • Turn off all electronic devices and place in backpack. • Take out all necessary materials (planner, binder, pencil) and place back pack on floor under desk. • Read the Smart Board and follow all directions posted. Copy homework assignment into planner. • Use a white board to complete any bell work that is assigned.

2. BELLWORK Write in set notation and graph the following solutions: A. B. C.

3. Lesson 12 Solving Equations Homework: S.67 #’s 1-6, 9-14, 17

4. STUDENT OUTCOME The student will…. • Be introduced to the formal process of solving an equation • Be able to explain each step of the properties of equality • Be able to identify equations that have the same solution.

5. Exercise 1: (page S.63) • Use the commutative property to write an equation that has the same solution set as: B. Use the associative property to write an equation that has the same solution set as: C. Does this reasoning apply to the distributive property as well?

6. Exercise 2: (S.64) Consider the equation: • Verify that this has the solution set {-3,2}. Draw this solution set as a graph on the number line. We will later learn how to show that these happen to be the ONLY solutions to this equation. B. Let’s add four to both sides of the equation and consider the new equation . Verify 2 and -3 are still solutions. C. Let’s now add x to both sides of the equation and consider the new equation. Are -3 and 2 still solutions? continued on next slide

7. Exercise 2: continued Consider the equation: D. Let’s add - 5to both sides of the equation and consider the new equation . Are 2 and -3 still solutions? E. Let’s multiply both sides by ⅙ to get /6 =1. Are 2 and -3 still solutions? F. Let’s go back to part (d) and add to both sides of the equation and consid the new equation Are 2 and -3 still solutions?

8. Exercise 3: (S.65) • Solve for r: 3/2r = 1/4 B. Solve for s: C. Solve for y: 4y - 3 = 5y -8

9. Exercise 4: (S.65) Consider the equation Solve for x using the given starting point. Group 1: Subtract 3x from both sides. Group 2: Subtract 4 from both sides. Group 3: Subtract 8x from both sides. Group 4: Add 16 to both sides.

10. Closing (page S.66) Consider the equation . Solve for using the given starting point. • Use the commutative property to create an equatio wit hthe same solution set. B. Using the result from (a), use the associative property to create an equation with the same solution set. C. Using the result from (b), use the distributive property to create an equation with the same solution set.

11. Lesson Summary If is a solution to an equation, it will also be a solution to the new equation formed when the same number is added to (or subtracted from) each side of the original equation or when the two sides of the original equation are multiplied by (or divided by) the same non-zero number. These are referred to as the Properties of Equality. If one is faced with the task of solving an equation, that is, finding the solution set of the equation: Use the commutative, associative, and distributive properties, AND use the properties of equality (adding, subtracting, multiplying by non-zeros, dividing by non-zeros) to keep rewriting the equation into one whose solution set you easily recognize. (We believe that the solution set will not change under these operations.)

12. EXIT TICKET Determine which of the following equations have the same solution set by recognizing properties, rather than solving. • 2x + 3 = 13 - 5x b. 6 + 4x = -10x + 26 c. 6x + 9 = 13/5 - x d. .6 + .4x = -x + 2.6 e. 3(2x + 3) = 13/5 - x f. 4x = -10x + 20 g. 15(2x + 3) = 13 - 5x h. 15(2x +3) + 97 = 110 - 5x