Lesson 3.2: Introduction to Solving Equations PowerPoint Companion Slides 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/

3). 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 x = 8.25 3 = 8.25

Two bottles of root beer and a $3 ice cream cost a total 4). 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

5). 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

2). Current Value Instructions Algebra Tiles 5 8 16 10 5 a). Pick any number. x 5 8 b). Now add 3. c). Multiply that answer by 2. 16 d). Subtract 6 from that answer. 10 e). Divide that answer by 2. 5

2). Current Value Instructions Algebra Tiles 5 8 16 10 5 a). Pick any number. x 5 x 1 1 1 8 b). Now add 3. c). Multiply that answer by 2. 16 d). Subtract 6 from that answer. 10 e). Divide that answer by 2. 5

2). Current Value Instructions Algebra Tiles 5 8 16 10 5 a). Pick any number. 5 8 b). Now add 3. c). Multiply that answer by 2. 16 d). Subtract 6 from that answer. 10 e). Divide that answer by 2. 5

2). Current Value Instructions Algebra Tiles 5 8 16 10 5 a). Pick any number. 5 8 b). Now add 3. c). Multiply that answer by 2. 16 d). Subtract 6 from that answer. 10 e). Divide that answer by 2. 5

2). Current Value Instructions Algebra Tiles 5 8 16 10 5 a). Pick any number. 5 8 b). Now add 3. c). Multiply that answer by 2. 16 d). Subtract 6 from that answer. 10 e). Divide that answer by 2. 5

Original number 2). Current Value Instructions Algebra Tiles 5 8 16 10 Pick any number. 5 8 b). Now add 3. Original number c). Multiply that answer by 2. 16 d). Subtract 6 from that answer. 10 e). Divide that answer by 2. 5 Final picture:

Keeping an Equation Balanced Fill out this part of your handout as we go over it, please.

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

2 rules to follow when solving equations The goal is to… To keep the equation balanced, you have to…

Let’s practice solving equations using algebra tiles.

7). 2x + 3 = 9

7). 2x + 3 = 9

7). 2x + 3 = 9 Draw this on your handout

Draw this on your handout. 7). 2x + 3 = 9 Draw this on your handout. Take away Take away What can you do to both sides that will get an x by itself?

7). 2x + 3 = 9 Draw this on your handout

7). 2x + 3 = 9 How much is each x worth? x = 3

Always look at the original picture to check the answer. 7). 2x + 3 = 9 Let’s check our answer x = 3 3 Always look at the original picture to check the answer. 3

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 = ___

7). 2x + 3 = 9 3 3 Total = 9 Total = 9 What do you think would happen if you substitute any other value for x (instead of 3)?

Watch and discuss the steps of #8 so you can do #9 on your own.

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

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

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

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

Always to back to the original picture to check. 8). 1 + 4x = 7 + 3x Check your answer x = 6 Always to back to the original picture to check.

The answer to the check step is part of your answer. Not optional! 8). 1 + 4x = 7 + 3x Check your answer x = 6 6 6 6 6 6 6 6 Total = ___ 1 + 24 Total = ___ 7 + 18 Total = 25 Total = 25 The answer to the check step is part of your answer. Not optional! 25 = 25

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

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

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

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

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

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

10). 2 + 5x = 2x + 14 Take away Take away Take away Take away x = 4

Let’s check our answer 10). 2 + 5x = 2x + 14 Total = ___ 2+ 20 Total = 8 + 14 Total = 22 Total = 22 Check: 22 = 22 x = 4