Solving Equations

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How Do We Solve Two-Step Equations Using Algebra?

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SOLVE: 3x – 8 = 7 Let us start with an example:

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Solving Equations When solving expressions we used Please Excuse My Dear Aunt Sally P E D M A S When solving EQUATIONS we reverse the order

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Now lets think of our equation as a balance with our center point being the equals sign. 3x – 8 = 7 3 – 8 = 7 S A D M E P There are two operations on the left side of the balance. Multiplication Subtraction

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+ 8 S A D M E P Multiplication Subtraction We undo subtraction before we undo multiplication. To undo subtraction we use the opposite operation, addition. To undo multiplication we use the opposite operation, division. 3x = 7 – 8 Since we added 8 to the left side, this side is now heavier and the scale will be thrown out of balance. To get the scale back in balance we must now add 8 to the right side. + 8 3x = 15 ÷ 3 x = 15 Since we divided the left side by 3, this side is now lighter and the scale will be thrown out of balance. To get the scale back in balance we must now divide the right side by 3. ÷3 x = 5

x = 5