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Algebra Equations with x on both sides © Victoria Smith Begin

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Equations with x on both sides 10x – 7 = 6x + 5 © Victoria Smith Next

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Equations with x on both sides 10x – 7 = 6x x First, we want to get all of the x’s on one side of the equation. Remember, if the number we are moving is positive to start with, it becomes negative when we move it over, if it starts as negative, if becomes positive when we move it over. This gives us: 4x – 7 = 5 Summary 10x – 7 = 6x + 5 4x – 7 = 5 © Victoria Smith Next

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Equations with x on both sides 4x – 7 = 5 +7 Now, we want to get all of the numbers on the other side of the equation. Again remember that if the number we are moving is positive to start with, it becomes negative when we move it over, if it starts as negative, if becomes positive when we move it over. This gives us: 4x = 12 Summary 10x – 7 = 6x + 5 4x – 7 = 5 4x = 12 © Victoria Smith Next

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Equations with x on both sides 4x = 12 ÷ 4 In the last stage, if a number was negative, we did the opposite to it when it moved. The same rule applies when it is multiplied (the opposite is divide). So on the left side, you are multiplying by 5, this becomes divide by 5 when it moves to the other side. This gives us: x = 3 Summary 10x – 7 = 6x + 5 4x – 7 = 5 4x = 12 x = 3 © Victoria Smith Next

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Equations with x on both sides 8x – 3 = 3x + 1 Not every equation will give you an integer (whole number) as a value for x when solved. Let’s work through this one to see what happens: © Victoria Smith Next

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Equations with x on both sides 8x – 3 = 3x x First, we want to get all of the x’s on one side of the equation. Remember, if the number we are moving is positive to start with, it becomes negative when we move it over, if it starts as negative, if becomes positive when we move it over. This gives us: 5x – 3 = 1 Summary 8x – 3 = 3x + 1 5x – 3 = 1 © Victoria Smith Next

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Equations with x on both sides 5x – 3 = 1 +3 Now, we want to get all of the numbers on the other side of the equation. Again remember that if the number we are moving is positive to start with, it becomes negative when we move it over, if it starts as negative, if becomes positive when we move it over. This gives us: 5x = 4 Summary 8x – 3 = 3x + 1 5x – 3 = 1 5x = 4 © Victoria Smith Next

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Equations with x on both sides 5x = 4 ÷ 5 In the last stage, if a number was negative, we did the opposite to it when it moved. The same rule applies when it is multiplied (the opposite is divide). So on the left side, you are multiplying by 5, this becomes divide by 5 when it moves to the other side. This gives us: x = 4 / 5 Summary 8x – 3 = 3x + 1 5x – 3 = 1 5x = 4 x = 4 / 5 © Victoria Smith Next

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Equations with x on both sides 7x – 3 = 3x x First, we want to get all of the x’s on one side of the equation. Remember, if the number we are moving is positive to start with, it becomes negative when we move it over, if it starts as negative, if becomes positive when we move it over. This gives us: 4x – 3 = 8 Summary 7x – 3 = 3x + 8 4x – 3 = 8 © Victoria Smith Next

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Equations with x on both sides 4x – 3 = 8 +3 Now, we want to get all of the numbers on the other side of the equation. Again remember that if the number we are moving is positive to start with, it becomes negative when we move it over, if it starts as negative, if becomes positive when we move it over. This gives us: 4x = 11 Summary 7x – 3 = 3x + 8 4x – 3 = 8 4x = 11 © Victoria Smith Next

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Equations with x on both sides 4x = 11 ÷ 4 In the last stage, if a number was negative, we did the opposite to it when it moved. The same rule applies when it is multiplied (the opposite is divide). So on the left side, you are multiplying by 5, this becomes divide by 5 when it moves to the other side. This gives us: x = 11 / 4 Summary 8x – 3 = 3x + 1 5x – 3 = 1 5x = 4 x = 11 / 4 © Victoria Smith Next

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Equations with x on both sides You must also remember to give fractions in their lowest or simplest terms, so x = 11 / 4 becomes: x = 2 3 / 4 Summary 8x – 3 = 3x + 1 5x – 3 = 1 5x = 4 x = 11 / 4 x = 2 3 / 4 © Victoria Smith

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