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**Solving One and Two step Equations**

Sol A.1

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**Why do we do the same thing to both sides of an equation**

Discuss that you must keep it balanced. If I give one daughter 20 dollars then I need to give the other daughter 20 dollars. If I give the left side of the room 5 points on a test I need to give the right side of the room 5 points.

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**Why do we do the same thing to both sides of an equation**

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**Think of this equation as a balance scale.**

Ex. 1) Solve r + 16 = -7 Think of this equation as a balance scale. r + 16 -7 = Whatever you do to one side has to be done to the other to keep it balanced!

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1) Solve r + 16 = -7 To solve, you must get the variable by itself. What number is on the same side as r? 16 To get r by itself, we must undo the “add 16”. What is the opposite of addition? Subtract 16

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1) Solve r + 16 = -7

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1) Solve r + 16 = -7 r = -23 = -7 Draw “the river” to separate the equation into 2 sides Subtract 16 from both sides Simplify vertically Check your answer by substituting your answer back into the problem

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Ex. 2) Solve x + 2 = -3

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2) Solve x + 2 = -3 x = -5 = -3 Draw “the river” to separate the equation into 2 sides Subtract 2 from both sides Simplify vertically Check your answer by substituting your answer back into the problem On homework and tests, be sure to check your work!! There is no reason why you should miss a problem!

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**Addition and subtraction Properties of Equality**

Definition: Either adding or subtracting the same number to each side of the equation produces an equivalent equation. Example: X - 9 = 15 How can you check your answers?

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**Try These: Don’t forget to check your answer**

m + 17 = 3 b – (-4) = 9

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r – 2 = 21

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m + 17 = 3

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b – (-4) = 9

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**Multiplication and Division Properties of Equality**

Definition: If you multiply or divide each side of the equation by the same nonzero number you produce an equivalent equation. Example 6: Multiplication:

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Division: Example 7. 7m=91

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Try These: 8. -6m = = -x 10.

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-6m = 48

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14 = -x

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10.

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**Solving Equations using Reciprocals**

Rule – When the original number is multiplied by it’s reciprocal the product should equal 1. Example 11: Don’t forget to check your answer

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Example 12

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**Solving Two Step Equations**

Note- When solving two step equations Always Isolate the variable first. (i.e. get rid of anything that is not with your variable.) Example 13:

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**Solving Two Step Equations**

Example 14:

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Try These:

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15.

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**Solving Two-Step equations by combining like terms**

Example: 18. 7x – 4x = b – 7b = 4

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