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Solving Equations

Solving Equations. Involving One Operation. A Question of Balance. The two sides on a balanced scale must be equal to each other. E + 6 = 11. E = 5. What does the Egg weigh?. A Question of Balance. The two sides of an equation are equal to each other.

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Solving Equations

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  1. Solving Equations Involving One Operation

  2. A Question of Balance The two sides on a balanced scale must be equal to each other E + 6 = 11 E= 5 What does the Egg weigh?

  3. A Question of Balance The two sides of an equation are equal to each other The left side and the right side must be balanced 2(3) + 4 10 When you do something to one side of an equation, You have to do the same thing to the other side.

  4. A Question of Balance If the two sides of an equation are not equal… 3(7) – 2 20 + 1

  5. A Question of Balance If the two sides of an equation are not equal… Then it is not balanced! 3(7) – 2 20 + 1

  6. A Question of Balance What happens if we change one of the sides of a balanced equation? 8 + 3 +1 8 + 3 + 1 11 Then it is not balanced!

  7. A Question of Balance What happens if we change one of the sides of a balanced equation? + 1 11 8 + 3 + 1 We need to make the same change to the other side! Then it is not balanced!

  8. A Question of Balance What happens if we change one of the sides of a balanced equation? 8 + 3 + 1 11 + 1 The 11th Commandment (for equations): We need to make the same We need to make the same change to the other side! change to the other side! Whatever thou dost unto the left, thou also must do unto the right.

  9. To solve an equation means to find every number that makes the equation true. We do this by adding or subtracting to each side of the equation … but always keep it balanced!

  10. Example: 1 In the equation, 7 added to a number gives 15… Solving the equation means, finding the value of the variable that makes the equation true. Let’s go back to the balance

  11. The 11th Commandment (for equations): Whatever thou dost unto the left, thou also must do unto the right. x + 7 - 7 15 - 7 Subtract 7 from both sides Simplify both sides

  12. x 8 The 11th Commandment (for equations): Whatever thou dost unto the left, thou also must do unto the right. Subtract 7 from both sides Simplify both sides Now we know the value of x

  13. x 8 The 11th Commandment (for equations): Whatever thou dost unto the left, thou also must do unto the right. So the solution goes like this… x + 7 = 15 x + 7 – 7 = 15 – 7 Subtract 7 from both sides Simplify both sides x = 8 Now we know the value of x

  14. = 3 In some equations,the solution is obvious. x – 7 = 12 5n = 35 x = 19 n = 7 20 + h = 41 h = 21 c = 24 We can simply work the operation backwards in our head to get the answer.

  15. But in other equations, the solution is not so obvious. We have to know what operation(s) must be done to solve it, and work it out carefully.

  16. The opposite of multiplying by is multiplying by But in other equations, the solution is not so obvious. You have to do the inverse operation to both sides to get the variable by itself Ex3. Ex2. The opposite of addition is subtraction The opposite of subtraction is addition Ex4. Ex5. The opposite of multiplication is division

  17. Multi-step equations When an equation has more than one operation you still have to isolate the variable by doing the following: • Make sure variable terms are all on one side, and constant terms are on the other. • Simplify • Divide by the coefficient of the variable.

  18. How would we solve 3x + 5 = 12? Let’s take another look at the balance Ex.6 3x + 5 – 5 – 5 12 Subtract 5 from both sides

  19. How would we solve 3x + 5 = 12? Let’s take another look at the balance 3x 7 Subtract 5 from both sides Simplify

  20. How would we solve 3x + 5 = 12? Let’s take another look at the balance 7 3x 3 3 Subtract 5 from both sides Simplify Divide both sides by coefficient of the variable (3)

  21. So the solution is: How would we solve 3x + 5 = 12? Let’s take another look at the balance 7 x 3 Subtract 5 from both sides Simplify Divide both sides by coefficient of the variable (3)

  22. Let’s try some more equations Remember, we have to keep the equations balanced! Solve: 8m–10=36 Ex8. Ex7. 8m–10+10=36+10 8m=46 8 8 m= w=84

  23. Ex9. Notice that there are variables on both sides 5x  2 = x + 4 Solve: Get rid of the -2 on the left side 5x  2 + 2 = x + 4 + 2 5x = x + 6 Simplify Get rid of the x on the right side 5x – x = x – x + 6 4x = 6 Simplify Get rid of the cofficient of x 4 4 Simplify x =

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