Lesson 3.2: Introduction to Solving Equations PowerPoint 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 + = 28.75 3x + 4.00 = 28.75 24.75 4.00 ? _________ = 24.75 3x = 24.75 24.75 = 8.25 3 x = 8.25 = 8.25

Two bottles of root beer and a $3 ice cream cost a total Worked Example Two bottles of root beer and a $3 ice cream cost a total of $8.40. How much is each bottle? Picture Equation + 3.00 = 8.40 2x + 3.00 = 8.40 5.40 ? _________ = 5.40 2x = 5.40 5.40 = 2.70 2 = 2.70 x = 2.70

6). What is x worth in the picture below? Equation 91 = 5 + x 91 = 5 + 4x 86 ? _________ 86 = x 86 = 4x 86 = 21.5 4 21.5 = x 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? 3 3 3 2 + 3 3 2 + 3 2 + 3 2 + 3

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

Let’s practice solving equations using your algebra tiles.

7). 2x + 3 = 9

7). 2x + 3 = 9

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

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

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

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

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

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

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

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

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

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

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

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

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

9). 1 + 2x = 4x

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

9). 1 + 2x = 4x How much is each x worth? x = half of 1 ?? x = 0.5

9). 1 + 2x = 4x Let’s check our answer x = 0.5

9). 1 + 2x = 4x 0.5 0.5 0.5 0.5 Let’s check our answer 0.5 0.5 x = 0.5

Let’s check our answer 9). 1 + 2x = 4x x = 0.5 Total = ___ 1 + 1

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

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

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

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

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

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