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**Using Inverse Operations**

6.1 Solving Equations by Using Inverse Operations

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**To ‘undo’ a sequence of operations…**

… we perform the inverse operations in the reverse order. For example, compare the steps and operations to wrap a present with the steps and operations to unwrap the present: 1. Put present in box 2. Wrap box 3. Put on ribbon 3. Take present out of box 2. Unwrap box 1. Take off ribbon

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**Inverse Operations… SUBTRACTION Addition & MULTiPLICATION & Division**

… ‘undo’ or reverse each other’s results. In order to be able to solve equations, you MUST know the mathematical inverse operations: SUBTRACTION Addition & MULTiPLICATION & Division

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**We can use inverse operations to solve equations…**

… to do this, we determine the operations that were applied to the variable to build the equation. We then use INVERSE OPERATIONS to isolate the variable by ‘undoing’ these operations.

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**What is the inverse operation?**

Here’s an example… Your job is to figure out the value of ‘x’. In this example, finding ‘x’ is easy, but we need a strategy to determine ‘x’ when the questions get harder! What mathematical operations have been applied to the variable to build this equation? + 5 BUILD x x + 5 SOLVE 13 x = 8 What is the inverse operation? - 5

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**Let’s look at a few more examples:**

BUILD x x – 3 t 7t SOLVE 9 21 x = 12 t = 3 What does the ‘math’ look like when we solve these equations?

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**How can you check to see if you are correct?**

Let’s try a harder one… x 4.5 - 3.2 BUILD d 4.5d 4.5d – 3.2 SOLVE d = -3.4 -15.3 -18.5 How can you check to see if you are correct? ÷ 4.5 + 3.2 Inverse Operations!

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**Have you noticed a connection between solving equations and BEDMAS?**

Here’s a few more… Make sure you ‘build’ the equation first and then use the inverse to solve! Have you noticed a connection between solving equations and BEDMAS?

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**Here’s the hardest one yet!**

+1 x 7 ÷2 x x + 1 7(x + 1) x = 3 4 28 14 - 1 ÷ 7 x 2 The KEY thing to remember about solving any equation is: Whatever you do to one side of an equation, you must do to the other side to keep the equation balanced!

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**How about a ‘word problem’? **

A rectangle has length 3.7 cm and perimeter 13.2 cm. Write an equation that can be used to determine the width of the rectangle. Solve the equation. Verify (check) your solution.

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**What does OF mean in math?**

Working with %... Seven percent of a number is 56.7. Write, then solve an equation to determine the number. Check the solution. Choose the method that works best for you, but you MUST show an equation! What does OF mean in math?

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Assignment Time! Page 271: 5ab, 6ac, 7 (discuss), 8be, 9ab, 10bcf, 11ad, 12 (discuss), 13abc, 14abc, 16ab, 17ab, 18acd (be prepared to go over in class!)

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**What are the rules for solving equations?**

Build the equation (either on paper) or in your mind. Whatever operation you do to one side, you MUST do to the other side in order to keep the equation balanced! ALWAYS CHECK YOUR WORK!

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Literal Equations. Let’s begin by thinking about numerical equations… Here are two numerical equations that uses the same values. 15 = 12 + 3 12 = 15.

Literal Equations. Let’s begin by thinking about numerical equations… Here are two numerical equations that uses the same values. 15 = 12 + 3 12 = 15.

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