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**One Step Equations Solving Equations using Addition and Subtraction**

Algebra Seminar

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**How to Solve an Equation**

r + 16 -7 = Think of equations as a balance of two things. The left side and right side of the equation must be equal. Whatever you do to one side has to be done to the other to keep it balanced! Our goal = To make both sides of the equation equal!

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Vocabulary * A variable is a letter which represents an unknown number. Any letter can be used as a variable. * An algebraic expression contains at least one variable. Examples: a, x+5, 3y – 2z * A verbal expression uses words to translate algebraic expressions. Example: “The sum of a number and 3” represents “n+3.” * An equation is a sentence that states that two mathematical expressions are equal. Example: 2x-16=18

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**Steps to Solving Equations**

1. Simplify each side of the equation, if needed, by distributing or combining like terms. 2. Move variables to one side of the equation by using the opposite operation of addition or subtraction. 3. Isolate the variable by applying the opposite operation to each side. First, use the opposite operation of addition or subtraction. Second, use the opposite operation of multiplication or division. 4. Check your answer.

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**When we solve an equation, we will use “opposite operations”.**

Addition/Subtraction x + 8 = 2 x = -6 y - 13 = -4 y = 9

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**When solving equations, we want to simplify the equation to make it as easy as possible.**

y + (-3) = 8 is rewritten as y – 3 = 8 p – (-5) = 6 is rewritten as p + 5 = 6 As a general rule, replace “+ (- )” with “–” and “– (- )” with “+”. This will make things less confusing in the future!

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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 When we subtract 16 on both sides we know that r = -23!

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Solve. w + 14 = -8

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Solve. y + (-10) = 6

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Solve. -11 = a + 8

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Solve. -13 + h = -5

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Solve. -7 = k

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Solve. m - (-13) = 37

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Solve. z + (-13) = -27

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Solve. p - (-27) = 13

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Solve. 41 = 32 + r

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Solve. d + 16 = 14

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Solve. x + 15 = -6

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**To solve this problem we should Make a Plan and Write an Equation.**

Real World Equations Sarah heard on the morning news that the temperature had dropped 26 degrees since midnight. In the morning, the temperature was –8°F. What was the temperature at midnight? To solve this problem we should Make a Plan and Write an Equation. Let t be our variable to represent the temperature at midnight and use the equation model, so t – 26 = -8. If we add 26 to both sides, we see that the temperature at midnight was 18 degrees!

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