Using Reverse Order of Operation

Warm Up 1.-4  (-3) 2.6  (-7)  (- 2) ÷ (-4) ÷ (-3) + 6

Objectives Use variables and appropriate operations to write an equation that represents a verbal description. (AF 1.1) * * * Solve simple equations in one variable over the integers. (AF 4.0) Solve problems that involve profit. (NS 1.7)

Objectives * * I can solve one-step equations. I can solve a word problem that uses a one-step equation.

Solving Equation Using Reverse Order of Operation ( ) + X 

Order of operations: y lease xcuse ear unt ally

Add + Subtract - Multiply x Divide  Please Excuse My Dear Aunt Sally P E MDMD ASAS Parentheses ( ) Exponents 4²

3 + 7(10 - 4) = Solve within Parenthesis (10 - 4)= 6 Multiple 7(6)= 42 Add = 45

10 = 10

(10-4) = 6

7(10-4) = 42

3 + 7(10-4) = 45

Reverse Order of Operations Add/Subtract (L to Right)outside parentheses Multiply/Divide (L to Right)outside parentheses Exponents Parenthesis/Brackets

Add + Subtract - Multiply x Divide  Please Excuse My Dear Aunt Sally P E MDMD ASAS Parentheses ( ) Exponents 4 3

3 + 7(x - 4) = 45 Subtract 3 = 42 Divide by 7 = 6 Add 4 = 10 x = 10

3 + 7(x-4) = 45

45-3 = 42

42 ÷ 7 = 6

6 + 4 = 10

x = 10

A Question of Balance The two sides on a balanced scale must be equal to each other What does the Egg weigh? E + 6 = 11 E = 5

When you do something to one side of an equation, You have to do the same thing to the other side. A Question of Balance 2(3) The two sides of an equation are equal to each other The left side and the right side must be balanced

A Question of Balance If the two sides of an equation are not equal… 3(7) –

A Question of Balance If the two sides of an equation are not equal… 3(7) – Then it is not balanced!

A Question of Balance What happens if we change one of the sides of a balanced equation? Then it is not balanced!

A Question of Balance What happens if we change one of the sides of a balanced equation? Then it is not balanced! We need to make the same change to the other side! + 1

We need to make the same change to the other side! What happens if we change one of the sides of a balanced equation? A Question of Balance We need to make the same change to the other side! Whatever thou dost unto the left, thou also must do unto the right. The 11 th Commandment (for equations):

To solve an equation means to find every number that makes the equation true. We do this by doing the inverse operation to each side of the equation … but always keep it balanced!

In the equation, 7 added to a number gives 15… Solving the equation means, finding the value of the variable that makes the equation true. Let’s go back to the balance

x Whatever thou dost unto the left, thou also must do unto the right. The 11 th Commandment (for equations): - 7 Subtract 7 from both sides Simplify both sides

Whatever thou dost unto the left, thou also must do unto the right. The 11 th Commandment (for equations): x 8 Subtract 7 from both sides Simplify both sides Now we know the value of x

x 8 Subtract 7 from both sides Simplify both sides Now we know the value of x Whatever thou dost unto the left, thou also must do unto the right. The 11 th Commandment (for equations): So the solution goes like this… x + 7 = 15 x + 7 – 7 = 15 – 7 x = 8

Think of the situation like this: There is a house with two rooms One room has an “x” in it, the other does not x + 5 The wall between the rooms is where the “=“ sign is. = 7

We need to get the “x” ALONE! which object Identify which object is in the “x” room Object to move: the “5” x + 5 = 7 Which operation Which operation ( +, -, x,  ) is attaching the “5” to the “x”? We must use the Inverse Operation Operation being used: “+” Opposite of “+”: “ - ” So we must subtract 5 to get the “x” alone in his room.

x + 5 = 7 Now that we know what to do, How do we do it? We know we must subtract the “5” to get rid of it. But in equations, whatever you do to one side, you must also do to the other side. This keeps the equation “balanced”. So we will subtract 5 from each side of the equal sign.

x + 5 = 7 Subtract 5 from each side On the left, = 0 On the right, = 2 x = x = 2 Once the “x” is alone on one side, the other side is the answer. ANSWER:

Multiplication & Division Equations

We need to get the “x” ALONE! which object Identify which object is in the “x” room Object to move: the “2” 2x = 16 Which operation Which operation ( +, -, x,  ) is attaching the “2” to the “x”? We must use the Inverse Operation Operation being used: “x” Opposite of “x”: “  ” So we must divide by 2 to get the “x” alone in his room. Note: when a number sits next to a variable with nothing in between the two, the operation is multiplication. (two times “x”) is written as “2x”.

2x = 16 Divide each side by two On the left, 2 ÷ 2 = 1 On the right, 16 ÷ 2 = 8 x = 8 Once the “x” is alone on one side, the other side is the answer. ANSWER: 2x = If a number sits next to a variable with nothing in between the two, the operation is multiplication. We show division by using fraction bars.

We need to get the “x” ALONE! which object Identify which object is in the “x” room Object to move: the “2” x = 8 Which operation Which operation ( +, -, x,  ) is attaching the “2” to the “x”? We must use the Opposite Operation Operation being used: “  ” Opposite of “  ”: “x” So we must multiply by 2 to get the “x” alone in his room. Note: When a number is written as a fraction, the operation is division. (“x” divided by 2) is written as “x/2”. 2

Multiply each side by 2 On the left, 2 ÷ 2 = 1 On the right, 8 x 2 = 16 x = 16 Once the “x” is alone on one side, the other side is the answer. ANSWER: x = (2)

In some equations, the solution is obvious. x – 7 = 12 x = 19 5n = 35 n = h = 41 h = 21 = 3 c = 24 We can simply work the operation backwards in our head to get the answer.

But in other equations, the solution is not so obvious. We have to know what operation(s) must be done to solve it, and work it out carefully.

You have to do the inverse operation to both sides to get the variable by itself The opposite of addition is subtraction The opposite of subtraction is addition The opposite of multiplying by is multiplying by The opposite of multiplication is division

Flow Map for Solving One Step Equations Isolate the variable Determine the operation Use the inverse operation

Flow Map for Solving One Step Equations Isolate the variable Determine the operation Use the inverse operation ÷ (-2) · (-2)

Flow Map for Solving One Step Equations Isolate the variable Determine the operation Use the inverse operation

Use a flow map to solve