1. Algebra Solving Equations

2. What does the egg weigh? The Two Sides of an Equation Must be Balanced

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

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

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

6. Solving an Equation 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!

7. Solving an Equation 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. A general rule is to have all the variables on the left hand side of the equal sign and the constants on the right hand side. Let’s go back to the balance

8. x + 7 15 - 7 Subtract 7 from both sides Simplify both sides Solving an Equation x 8 Now we know the value of x

9. x 8 So the solution goes like this… x + 7 = 15 x + 7 – 7 = 15 – 7 x = 8 Balancing an Equation Letters left, numbers right

10. Multi-step equations When and 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.

11. 3x + 5 11 – 5 Subtract 5 from both sides How would we solve 3x + 5 = 11? Using the balance Solving an Equation Divide both sides by the coefficient of the variable (3) 6 3x 33

12. Balancing an Equation 2 x

13. Notice that there are variables on both sides Get rid of the -2 on the left side Simplify Get rid of the x on the right side Get rid of the coefficient of x

14. Forming Equations Its important to associate common words with their equivalent meaning in maths. Addition increased by more than combined, together total of sum added to Greater than When a certain number is increased by 5 the result is 12. x + 5 = 12 The sum of twice a certain number added to 3 is 17 3 + 2x = 17

15. Forming Equations Subtraction decreased by minus less difference between/of less than fewer than 3 less than a certain number is 5 x – 3 = 5 The difference between 3 times a certain number and 6 is 18 3x – 6 = 18

16. Forming Equations Multiplication of times multiplied by product of increased/decreased by a factor of (this type can involve both addition or subtraction and multiplication!) 4 times the sum of a certain number increased by 6 equals 32. 4(x + 6) = 32