Download 3-1 Solving Equations Using Addition and Subtraction

Solving Equations Using
Multiplication and Division
Objectives:
 A.4f Apply these skills to solve practical
problems.
 A.4b Justify steps used in solving equations.
 Use a graphing calculator to check your
solutions.
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.
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.
An easy example:
We all know that 3 = 3.  Would you ever put
deodorant under just one
arm?
Does 3(4) = 3? NO!
But 3(4) = 3(4).
The equation is still
true if we multiply
both sides by 4.
 Would you ever put nail
polish on just one hand?
 Would you ever wear just
one sock?
Let’s try another example!
x=4
2
Multiply each side
by 2.
(2)x = 4(2)
2
x=8
 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.
What do we do with negative fractions?
Recall that
x x
x
 

5
5
5
x
3.
Solve
5
Multiply both
sides by -5.
 The two negatives will
cancel each other out.
 The two fives will
cancel each other out.

x
(-5)
 3 (-5)
5
 x = -15
 Does -(-15)/5 = 3?
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 zeroand the equation will still hold true.
 Why did we add c ≠ 0?
2 Examples:
1) 4x = 24
Divide both sides by 4.
4x = 24
4
4
x=6
 Does 4(6) = 24? YES!
2) -6x = 18
Divide both sides by -6.
-6y = 18
-6
-6
y = -3
 Does -6(-3) = 18? YES!
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
Try these on your own...
x=3
7
4w = 16
y=8
-2
2x = 12
3
-2z = -12
3x = 9
-4
The answers...
x = 21
w= 4
y = -16
x = 18
z=6
x = -12