2. Solving Equations Using Multiplication and Division 4 A.4f Apply these skills to solve practical problems. 4 A.4b Justify steps used in solving equations. Objectives :

3. Remember, To Solve an Equation means... To isolate the variable having a coefficient of 1 on one side of the equation. Ex: x = 5 is solved for x. y = 2x - 1 is solved for y.

4. Multiplication Property of Equality For any numbers a, b, and c, if a = b, then ac = bc. What it means: You can multiply BOTH sides of an equation by any number and the equation will still hold true.

5. An easy example: We all know that 3 = 3. Does 3(4) = 3? NO! But 3(4) = 3(4). The equation is still true if we multiply both sides by 4. 4 Would you ever put deodorant under just one arm? 4 Would you ever put nail polish on just one hand? 4 Would you ever wear just one sock?

6. Let’s try another example! x = 4 2 Multiply each side by 2. (2)x = 4(2) 2 x = 8 4 Always check your solution!! 4 The original problem is x = 4 2 4 Using the solution x = 8, Is x/2 = 4? 4 YES! 4 = 4 and our solution is correct.

7. 4 The two negatives will cancel each other out. 4 The two fives will cancel each other out. (-5) 4 x = -15 4 Does -(-15)/5 = 3? What do we do with negative fractions? Recall that Solve. Multiply both sides by -5.

8. Division Property of Equality 4 For any numbers a, b, and c (c ≠ 0), if a = b, then a/c = b/c What it means: 4 You can divide BOTH sides of an equation by any number - except zero- and the equation will still hold true. 4 Why did we add c ≠ 0?

9. 2 Examples: 1) 4x = 24 Divide both sides by 4. 4x = 24 4 4 x = 6 4 Does 4(6) = 24? YES! 2) -6x = 18 Divide both sides by -6. -6x = 18 -6 -6 x = -3 4 Does -6(-3) = 18? YES!

10. A fraction times a variable: The two step method: Ex: 2x = 4 3 1. Multiply by 3. (3)2x = 4(3) 3 2x = 12 2. Divide by 2. 2x = 12 2 2 x = 6 The one step method: Ex: 2x = 4 3 1. Multiply by the RECIPROCAL. (3)2x = 4(3) (2) 3 (2) x = 6

11. Try these on your own...

12. The answers...

13. 9/12/13 Homework: Workbook page 20