Lesson 3 2 Introduction to Solving Equations Power

Lesson 3. 2: Introduction to Solving Equations Power. Point Companion Slides • These materials supplement the 3. 2 Lesson Packet, also available on Curriki. org • Problem numbers in the slides refer to the numbers in the packet. By Kevin Hall. This material can be used in its current form, customized, printed, and/or redistributed by the user under a Creative Commons 3. 0 Attribution Unported license. License terms available here: http: //creativecommons. org/licenses/by/3. 0/

4). You are having pizzas delivered. How much is each pizza? Picture Equation + 24. 75 ? _____ 24. 75 3 = 28. 75 3 x + 4. 00 = 28. 75 4. 00 = 24. 75 3 x = 24. 75 = 8. 25 x = 8. 25

Worked Example Two bottles of root beer and a $3 ice cream cost a total of $8. 40. How much is each bottle? Equation Picture + 3. 00 = 8. 40 2 x + 3. 00 = 8. 40 = 5. 40 2 x = 5. 40 = 2. 70 x = 2. 70 5. 40 ? _____ 5. 40 = 2. 70 2

6). What is x worth in the picture below? Picture 91 = 5 + x x x Equation x 91 = 5 + 4 x 86 ? _____ 86 = x x 86 = 4 x 86 = 21. 5 4 21. 5 = x

Keeping an Equation Balanced “ 2 + 3 = 5” means that 2 + 3 balances out with 5. 2+3 = 5

What will happen if we subtract something from ONLY this side? Discussion 2+3 5 3– 2

What will happen if we subtract something from ONLY this side? 2+3 3 What happens now?

What will happen if you subtract something from ONLY this side? 2 2+ +3 3 2+3 3 3

Do the same thing to both sides to keep the equation balanced. 2+3– 2 3 Scratch work 2+3– 2 5 – 2 3 5– 2 3

Let’s practice solving equations using your algebra tiles.

7). 2 x + 3 = 9

7). 2 x + 3 = 9

7). 2 x + 3 = 9 What can you do to both sides that will get an x by itself?

7). 2 x + 3 = 9 How much is each x worth? x=3 Keep these down here—we’ll use them to check our answer.

7). 2 x + 3 3 3 = 9 Let’s check our answer x=3 Always rebuild the original problem to check the answer.

7). 2 x + 3 3 3 Total = ___ = 9 Let’s check our answer

7). 2 x + 3 = 9 3 3 Total = 9 Let’s check our answer Total = ___

7). 2 x + 3 = 9 3 3 Total = 9 Was our answer correct, and why or why not?

8). 1 + 4 x = 7 + 3 x

8). 1 + 4 x = 7 + 3 x What can you do to both sides to get an x by itself?

8). 1 + 4 x = 7 + 3 x What can you do to both sides to get an x by itself?

8). 1 + 4 x = 7 + 3 x How much is each x worth? x=6

8). 1 + 4 x = 7 + 3 x Let’s check our answer x=6 Rebuild the original problem.

8). 1 + 4 x = 7 + 3 x Let’s check our answer x=6 8). Please do the “check step” on your own. Show your work on the handout.

8). 1 + 4 x = 7 + 3 x 6 6 6 6 Let’s check our answer x=6 Total = ___ 1 + 24 Total = ___ 7 + 18 Total = 25

9). 1 + 2 x = 4 x

9). 1 + 2 x = 4 x What can you do to both sides to get an x by itself?

9). 1 + 2 x = 4 x How much is each x worth? x = ? ? half of 1 x = 0. 5

9). 1 + 2 x = 4 x Let’s check our answer x = 0. 5

9). 1 + 2 x 0. 5 = 4 x 0. 5 Let’s check our answer x = 0. 5

9). 1 + 2 x 0. 5 Total = ___ 1+1 Total = 2 = 4 x 0. 5 Total = ___ 2 Let’s check our answer x = 0. 5

10). 2 + 5 x = 2 x + 14

10). 2 + 5 x = 2 x + 14 What can you do to both sides to get an x by itself?

10). 2 + 5 x = 2 x + 14 How much is each x worth? x=4

10). 2 + 5 x = 2 x + 14 Let’s check our answer x=4

10). 2 + 5 x 4 4 4 = 2 x + 14 4 4 Total = ___ 2 + 20 Total = ___ 8 + 14 Total = 22 What can you do to both sides to get an x by itself?

Reflection Question 10). What arithmetic problem represents the picture below?