1. Solving Equations M7A2b Use the addition and multiplication properties of equality to solve one- and two-step linear equations.

2. What happened to the order of operations? Remember Please Excuse My Dear Aunt Sally? Parenthesis, Exponents, Multiply and Divide, Add and Subtract

3. Well….. Doesn’t it make sense that if we follow the order of operations to find the answer… that we do the order of operations backward, to find part of the missing problem when we already have the answer? Doesn’t it make sense that if we follow the order of operations to find the answer… that we do the order of operations backward, to find part of the missing problem when we already have the answer?

4. For example: Solve: 4(3) + 5 = x Solve: 4(3) + 5 = x First we’d multiply, then add 5. That makes x equal 17. First we’d multiply, then add 5. That makes x equal 17. What if you were given 4x + 5 = 17. What if you were given 4x + 5 = 17. Can we multiply first then add? Can we multiply first then add? Since we have the answer already, doesn’t it make sense to work backward to find the solution for x since x is the missing part of the problem? Since we have the answer already, doesn’t it make sense to work backward to find the solution for x since x is the missing part of the problem?

5. Inverse Operation Suppose you were on the phone with your friend who just gave you 20 numbers to add into your calculator, the 21 st number she gave you was 15 but you accidentally entered 115. Ooops! What can you do to fix the problem? Suppose you were on the phone with your friend who just gave you 20 numbers to add into your calculator, the 21 st number she gave you was 15 but you accidentally entered 115. Ooops! What can you do to fix the problem? Do you have to start all over again?

6. Applying the Inverse Operation An operation’s inverse is the operation that “undoes” the first operation. An operation’s inverse is the operation that “undoes” the first operation. For example, with the calculator problem, if you accidentally added 115, you can get back to where you were before you made the error if you subtract 115. For example, with the calculator problem, if you accidentally added 115, you can get back to where you were before you made the error if you subtract 115. Addition and subtraction are inverse operations. What other two operations are inverse operations? Addition and subtraction are inverse operations. What other two operations are inverse operations?

7. Using Inverse Operation to Solve Equations! Ready, Set, Go! Solve for x. 2(5x + 3) +4x -7 = 41

8. Just Kidding! We must take it one little step at a time. That is why we need to SHOW inverse operation on both sides of the equation, so we can see where we have been and what we have already done. We must take it one little step at a time. That is why we need to SHOW inverse operation on both sides of the equation, so we can see where we have been and what we have already done. Just nipping that question in the bud before I hear it a thousand times. Just nipping that question in the bud before I hear it a thousand times.

9. Now for Real Use inverse operation to solve the following equation: x + 6 = 10 Yeah, I know you know it is 4, but that’s not the point. The point is, can you do and show inverse operation on this small scale before you have to do it on a big problem like the one I showed you earlier, when whether you do it correctly or not isn’t as obvious. Yeah, I know you know it is 4, but that’s not the point. The point is, can you do and show inverse operation on this small scale before you have to do it on a big problem like the one I showed you earlier, when whether you do it correctly or not isn’t as obvious.

10. x + 6 = 10 The inverse of addition is subtraction, so subtract 6 from each side to find the value of x. The inverse of addition is subtraction, so subtract 6 from each side to find the value of x. x + 6 – 6 = 10 – 6 x = 4 x = 4 Check: 4 + 6 = 10 The solution is 4. The solution is 4.

11. Now you try! X + 3 = 12 Don’t forget to check!

12. Use addition to solve subtraction problems. x - 8 = 14 x - 8 + 8 = 14 + 8 x - 8 + 8 = 14 + 8 x = 22 x = 22 Check: 22 - 8 = 14

13. Now you try! x – 12 = 13 Don’t forget to check!

14. Add or Subtract? 15 - x = 6 Ask yourself, was 15 subtracted from anything? If we add 15, we’ll be subtracting x from 30, not 0. Ask yourself, was 15 subtracted from anything? If we add 15, we’ll be subtracting x from 30, not 0. 15 + 15 – x = 6 + 15 15 + 15 – x = 6 + 15 30 - x = 45 Wrong! Wrong!

15. The Correct Way to Do it! 15 - x = 6 15 - x = 6 15 – 15 – x = 6 - 15 - x = -9 - x = -9 So So x = 9 x = 9 Check: 15 – 9 = 6

16. Now you try! 20 – x = 16 Don’t forget to check!

17. Step-by-Step 1) Write the problem. 2) Show inverse operation on both sides of the equation. 3) Solve. 4) Check.

18. Neat Points Write only one equal sign on each line. Write only one equal sign on each line. Line the equal signs up, one under another. Line the equal signs up, one under another.