Solving EquationsSolving EquationsM7A2b Use the addition and multiplication properties of equality to solve one- and two-step linear equations.

What happened to the What happened to the order of operations?order of operations?Remember Please Excuse My Remember Please Excuse My

Dear Aunt Sally?Dear Aunt Sally?

Parenthesis, Exponents, Parenthesis, Exponents, Multiply and Divide, Add and Multiply and Divide, Add and

SubtractSubtract

Well…..Well…..

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

For example: For example: Solve: 4(3) + 5 = Solve: 4(3) + 5 = xx First we’d multiply, then add 5. That First we’d multiply, then add 5. That

makes makes xx equal 17. equal 17. What if you were given 4What if you were given 4xx + 5 = 17. + 5 = 17. Can we multiply first then add?Can we multiply first then add? Since we have the answer already, Since we have the answer already,

doesn’t it make sense to work doesn’t it make sense to work backward to find the solution for backward to find the solution for xx since since xx is the missing part of the problem? is the missing part of the problem?

Inverse OperationInverse Operation

Suppose you were on the phone with Suppose you were on the phone with your friend who just gave you 20 your friend who just gave you 20 numbers to add into your calculator, numbers to add into your calculator, the 21the 21stst number she gave you was 15 number she gave you was 15 but you accidentally entered 115. but you accidentally entered 115. Ooops! What can you do to fix the Ooops! What can you do to fix the problem?problem?

Do you have to start all over again?Do you have to start all over again?

Applying the Inverse OperationApplying the Inverse Operation An operation’s inverse is the operation An operation’s inverse is the operation

that “undoes” the first operation.that “undoes” the first operation. For example, with the calculator For example, with the calculator

problem, if you accidentally added 115, problem, if you accidentally added 115, you can get back to where you were you can get back to where you were before you made the error if you before you made the error if you subtract 115.subtract 115.

Addition and subtraction are inverse Addition and subtraction are inverse operations. What other two operations operations. What other two operations are inverse operations?are inverse operations?

Using Inverse Operation to Solve Using Inverse Operation to Solve Equations!Equations!

Ready, Set, Go!Ready, Set, Go!

Solve for Solve for xx..2(52(5xx + 3) +4 + 3) +4xx -7 = 41 -7 = 41

Just Kidding!Just Kidding!

We must take it one little step at a We must take it one little step at a time. That is why we need to SHOW time. That is why we need to SHOW inverse operation on both sides of the inverse operation on both sides of the equation, so we can see where we equation, so we can see where we have been and what we have already have been and what we have already done.done.

Just nipping that question in the bud Just nipping that question in the bud before I hear it a thousand times.before I hear it a thousand times.

Now for RealNow for RealUse inverse operation to solve the following Use inverse operation to solve the following

equation:equation:

xx + 6 = 10 + 6 = 10

Yeah, I know you know it is 4, but that’s Yeah, I know you know it is 4, but that’s not the point. The point is, can you do and not the point. The point is, can you do and show inverse operation on this small scale show inverse operation on this small scale before you have to do it on a big problem before you have to do it on a big problem like the one I showed you earlier, when like the one I showed you earlier, when whether you do it correctly or not isn’t as whether you do it correctly or not isn’t as obvious.obvious.

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

Now you try!Now you try!

XX + 3 = 12 + 3 = 12

Don’t forget to check!Don’t forget to check!

Use addition to solve subtraction Use addition to solve subtraction problems.problems.

xx - 8 = 14 - 8 = 14

xx - 8 + 8 = 14 + 8 - 8 + 8 = 14 + 8 xx = 22 = 22

Check: 22 - 8 = 14Check: 22 - 8 = 14

Now you try!Now you try!

xx – 12 = 13 – 12 = 13

Don’t forget to check!Don’t forget to check!

Add or Subtract?Add or Subtract?15 - 15 - xx = 6 = 6

Ask yourself, was 15 subtracted from Ask yourself, was 15 subtracted from anything? If we add 15, we’ll be anything? If we add 15, we’ll be subtracting x from 30, not 0.subtracting x from 30, not 0.

15 15 + 15+ 15 – – xx = 6 = 6 + 15+ 1530 - 30 - xx = 45 = 45 Wrong!Wrong!

The Correct Way to The Correct Way to Do it!Do it!

15 - 15 - xx = 6 = 615 – 15 – 15 – 15 – xx = 6 - 15 = 6 - 15

- - xx = -9 = -9 SoSo

xx = 9 = 9Check: 15 – 9 = 6 Check: 15 – 9 = 6

Now you try!Now you try!

20 – 20 – xx = 16 = 16

Don’t forget to check!Don’t forget to check!

Step-by-StepStep-by-Step

1)1) Write the problem.Write the problem.2)2) Show inverse operation on Show inverse operation on bothboth

sides of the equation.sides of the equation.3)3) Solve.Solve.4)4) Check.Check.

Neat PointsNeat PointsWrite only one equal Write only one equal sign on each line.sign on each line.

Line the equal signs Line the equal signs up, one under up, one under another.another.