3.2 – Solving Equations Using
Multiplication and Division
3.2 – Solving Equations Using
Multiplication and Division
Goal:
- I can solve one step linear equations using
multiplication and division.
Special Vocab… (from yeSterday)
Inverse Operations – are operations that undo each other, such
as addition and subtraction. Inverse operations help you
isolate the variable in an equation.
* Do the opposite to “undo” an equation!
 If you are adding TO the variable – then subtract.
 If subtracting FROM the variable – then add.
 If multiplying TO the variable, then divide!
 If dividing the variable BY something, then
multiply by the reciprocal!
Transformations that Produce
Equivalent Equations
Original Equation
Multiply each
side of the
equation by the
same nonzero
number.
Divide each
side of the
equation by the
same nonzero
number.
x
_
2
= 3
4x = 12
Equivalent Equation
x2
x=6
Divide by 4
x=3
Properties of
Equality
Multiplication Property of Equality – You can multiply both
sides of an equation by the same number and the statement
will still be true.
Numbers
Algebra
6=6
a=b
6(3) = 6(3)
a(c) = b(c)
18 = 18
Properties of
Equality
Division Property of Equality – You can divide both sides of
an equation by the same nonzero number, and the statement
will still be true.
Numbers
8 8
8=
8
4 4
2=2
Algebra
aa =bb c  0
c c
Practice: Solve the Equations
p
 10
5
y
13 
3
c
 56
8
Practice: Solve the Equations
7 x  56
16  4c
0.5k  10
Solving equations that contain fractions
Survival Tip – remember that dividing is the same
as multiplying by the reciprocal……
you may find it easier to multiply by a reciprocal
instead of dividing by a fraction.
5
v  35
9
Solving equations that contain
fractions
1 1
  b
4 5
1
w  102
6
4j 2

6
3
Weird Stuff SometimeS happenS……
3
t   15
4
The distance in miles from the airport that a plane
should begin descending, divided by 3, equals the
planes height above the ground in thousands of feet.
If a plane is 10,000 feet above the ground, write and
solve an equation to find the distance at which the
pilot should begin descending.
- What if a plane began descending 45 miles from the
airport? Find out how high the plane was flying when
the descent began.
Quick Review
• The inverse operation for multiplication is division,
and vice versa.
• The Properties of Equality are used to isolate the
variable on one side of the equation.
Homework
In your Textbook:
Page 190 #’s 1-8
Page 197 #’s 35-43