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Solving One-Step Equations 1.Addition & Subtraction Equations 2.Multiplication & Division Equations Author: Lynda Greene Copyright 2005 by Greenebox LLC

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Solving One-Step Equations To Solve an Equation, you will move terms from one side of the equal sign to the other. TOOL: Opposite Operations. The Three Simplest Opposite Operations: Addition and Subtraction Multiplication and Division Roots and Exponents GOAL: Get the “x” (the variable) alone on one side of the equal sign and everything else on the other side.

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Addition & Subtraction Equations

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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. = “x” wants to be completely alone in his room. So any other object in that room has to be moved to the other room, BY YOU! 7

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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 Opposite Operation Operation being used: “+” Opposite of “+”: “ - ” So we must subtract 5 to get the “x” alone in his room.

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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.

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

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We need to get the “x” ALONE! which object Identify which object is in the “x” room Object to move: the “8” x + 8 = 20 Which operation Which operation ( +, -, x, ) is attaching the “8” to the “x”? We must use the Opposite Operation Operation being used: “+” Opposite of “+”: “ - ” So we must subtract 8 to get the “x” alone in his room.

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x + 8 = 20 Subtract 8 from each side On the left, 8 - 8 = 0 On the right, 20 - 8 = 12 x + 8 - 8 = 20 - 8 x = 12 Once the “x” is alone on one side, the other side is the answer. ANSWER:

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We need to get the “x” ALONE! which object Identify which object is in the “x” room Object to move: the “9” 15 = x - 9 Which operation Which operation ( +, -, x, ) is attaching the “9” to the “x”? We must use the Opposite Operation Operation being used: “-” Opposite of “-”: “ + ” So we must add 9 to get the “x” alone in his room. Note: x can be on either side of the equal sign!

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15 = x - 9 Add 9 to each side On the left, 15 + 9 = 24 n the right, -9 + 9 = 0 15 + 9 = x - 9 + 9 24 = x Once the “x” is alone on one side, the other side is the answer. ANSWER:

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Multiplication & Division Equations

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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 Opposite 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”.

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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 = 16 2 2 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.

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-3x = 21 Divide each side by negative 3 On the left, (-3) ÷ (-3) = 1 On the right, 21 ÷ (-3)= -7 x = -7 Once the “x” is alone on one side, the other side is the answer. ANSWER: -3x = 21 -3 Note: Which operation is between the (-3) and the x. If a number sits next to a variable with nothing in between the two, the operation is multiplication.

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-32 = 4x Divide each side by 4 On the left, -32 ÷ 4 = -8 On the right, 4 ÷ 4 = 1 -8 = x Once the “x” is alone on one side, the other side is the answer. ANSWER: -32 = 4x 4 Note: The “x” can be on either side of the equal sign If a number sits next to a variable with nothing in between the two, the operation is multiplication.

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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

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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 = 8 2 2 (2)

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