1. Solving Equations Using Multiplication and Division
Objectives:
Apply these skills to solve practical problems.
Justify steps used in solving equations.
Use a graphing calculator to check your solutions.

2. 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.

3. 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.

4. An easy example: Would you ever put deodorant under just one arm?
Would you ever put nail polish on just one hand?
Would you ever wear just one sock?
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.

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

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

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

8. 2 Examples: 1) 4x = 24 Divide both sides by 4. 4x = 24 4 4 x = 6
x = 6
Does 4(6) = 24? YES!
2) -6x = 18
Divide both sides by -6.
-6y = 18
y = -3
Does -6(-3) = 18? YES!

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

10. Try these on your own...

11. The answers...