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Solving Equations

Solving Equations. Chapter 3.1. Part 1: Keeping it Equal. Keep the equation balanced around the equal sign X + 6 = 15. I want to play with this equation, so I am going to add 20 to the side with the 15…. So now I get X + 6 ? 35.

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Solving Equations

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  1. Solving Equations Chapter 3.1

  2. Part 1: Keeping it Equal Keep the equation balanced around the equal sign X + 6 = 15 I want to play with this equation, so I am going to add 20 to the side with the 15…. So now I get X + 6 ? 35 But wait, my equation is no longer equal so now I have to make it equal by now adding 20 to the other side of the equal sign… so now I get the equation X + 26 = 35 Note: I am allowed to do almost anything I want to an equation as long as I do the same thing to both sides of the equal sign

  3. Keeping it Equal • Here are some examples of what I can do to the equation: X + 6 = 15 I could Add 1000 to both sides to get: X + 1006 = 1015 Or I could instead Subtract 200 from both sides to get: X – 194 = -185 These three equations are all equal, because I have done the same thing to both sides. This is helpful to know, but currently adding 1000, and subtracting 200 did not help me to know what “x” is….

  4. Part 2: Solving by inverse operations • So now that we know we can do what ever we want to an equation as long as we do it to both sides of the equal sign, we now need to choose what we do to both sides. In the equation : X + 6 = 15 The best thing to do is to subtract 6 from both sides. Why are we subtracting 6? Because of what happens… we get X + 0 = 9 or X = 9 Note: By subtracting 6 from both sides we are doing what is called the “inverse operation”

  5. Inverse OperationsWhat are the inverse operations? Regular operations are… The inverse operations are… Addition Subtraction Subtraction Addition Division Multiplication Division Multiplication And more….. And more…..

  6. Part 3: Putting it together… so how does this work? • Problem…. X – 7 = 14 Step 1: Get the “x” by itself using inverse operation In this case since we are subtracting 7 we need to do the inverse and add 7 Step 2: Keep the equation equal Since we add 7 to one side we add it to the other side So we get…. X = 21

  7. What about this one…… • 4 – x = 12 Step 1: Get the “x” by itself using inverse operations How do I get rid of the 4? Since the 4 is positive we need to subtract 4 Step 2: Keep the equation equal Subtract 4 from both sides, which gives us: 0 – x = 8 or –x = 8 Problem!!!! I want my equation to say “x = something”, not “–x = something”…. What do I do now? Well… What if I decide to multiply both sides by “-1” This gives me (-1)-x = (-1)8 Which gives X = -8

  8. Or what about this one • t – (-4) = 8 Step 1: Get the “x” by itself using inverse operations Umm… What is the inverse operation going to be….. Well… Since I am subtracting a negative 4, I will Add a negative 4 Step 2: Keep the equation equal Adding negative 4 to both sides gives us t – (-4) + (-4) = 8 + (-4) which simplifies to t + 0 = 4 or t = 4

  9. Last pointer • With Every Single Equation you can always check your answer by putting it back into the original equation • Example…. With the equation x + 6 = 15 we got x = 9 so lets check…. Note: Whenever you substitute a value in for a variable you should always put it in parenthesis. Does (9) + 6 = 15? We get 15 = 15  With the equation 4 – x = 12 we got x = - 8 Does 4 – (-8) = 12? We get 12 = 12 

  10. Review • Remember: Keep equation balanced: Whatever you do to one side of an equation, you must do to the other side also Use Inverse operations to get the “variable” by itself Be certain to check your answer by putting it back into the original equation

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