1. Solving Equations

2. Inverse Operations  When solving equations algebraically, use the inverse (opposite) operation that is displayed to determine what value yhe variable (letter) has.

3. Opposite (inverse) operations:  Addition is the opposite of subtraction  Subtraction is the opposite of Addition  Multiplication is the opposite of Division  Division is the opposite of multiplication

4. Types of Equations:  There are five types of equations.  Type 1 (Adding) Type 1 (subtracting) X + 6 = 8 x – 8 = 4 X + 6 – 6 = 8 – 6 x – 8 + 8 = 4 + 8 X= 2 x = 12

5. Type 1 Equations ( Continued) Type 1 ( Multiplying) Type 1 (Division) 5x= - 35 x = -8 5x = -35 3 5 5 x * 3 = -8 * 3 X = - 7 3 x = -24 x = -24

6. Type 2 Equations Type 2 (adding) Type 2 (subtracting) 3x + 8 = 24 5x-3=12 3x + 8-8=24-8 5x-3+3= 12+3 3x= 16 5x= 15 3 3 5 5 X= 5 1/3 x= 3

7. Type 2 Equations (continued) Type 2 (Division) X + 5 = - 1.2 8 X +5 - 5 = -1.2 - 5 8 X = -6.2 8 X * 8 = -6.2 * 8 8 X= - 49.6

8. Type 3 Equations  A type 3 equation is one where there is more than one group of variables. To solve a type 3 equation, collect and place all the variables on the left of the equal sign, and all the constants on the right of the equal sign. Remember: When accomplishing this if a constant or variable crosses over the equal sign, change its sign to the opposite!!!!

9. Type 3 equations (Continued) 5x-3=3x+14 7x – 3x= 44 5x-3x=14+3 4x= 44 2x=17 4x = 44 2x = 17 4 4 2 2 x=11 X=8.5

10. Type 4 Equations A type 4 equation has one or more sets of brackets. Use the number on the outside of the bracket as a multiplier (distributive property), and multiply it by everything in the brackets. Once this is done, solve the equation normally.

11. Type 4 equations (Continued) 3(x+7)= - 39 3x + 21 = -39 3x + 21 – 21 = -39 – 21 3x = -60 3 3 X= -20

12. Another example (Type 4) 4(2X-5)=2(3X+6) 8X-20 = 6X+12 8X-6X = 12 + 20 2X = 32 2 2 X= 16

13. Ratio Type Equations A ratio type equation is classified as one in which there are two “fractions” on either side of the equal sign.

14. Ratio type equations (Continued) X = -3 6 2 2(x) = 6(-3) 2(x) = 6(-3) 2x = -18 2x = -18 2x = -18 2 2 X= -9

15. A more complicated Ratio type equation. 3x+5 = 7 4 2 2(3x+5) = 4(7) 6x+10 = 28 6x+10-10 = 28 – 10 6x= 18 6 6 X= 3