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LESSON 3.2 - Solving Equations Using Multiplication or Division
Goal: Solve equations using multiplication or division.
Warm-up:
Solve the equation. Show your steps!
1) x + 6 = -13
4) -4 + x = 15
2) 4 + x = 20
5) x – (-3) = 9
3) x – 9 = -11
6) x + (-5) = 10
Discuss the following two answers with your group and record your thoughts>
7) Why must equations be “balanced”?
8) How can writing algebraic equations make word problems easier to solve?
Multiplication Property of Equality
Words Multiplying each side of an equation by the same nonzero number produces an equivalent
equation.
x
x
Numbers If = 6, then
4=
4
4
4
Algebra If a = b and c  0, then ac =
.
EXAMPLE 1 - Solving an equation Using Multiplication
a)
t
8
=6
1
t
b)
3 = -12
3
4 x = 24
c)
Division property of Equality
Words Dividing each side of an equation by the same nonzero number produces an equivalent
equation.
3x
21
Numbers If 3x = 21, then
=
.
3
Algebra If a = b and c  0, then
a
c
=
.
EXAMPLE 2 - Solving an Equation Using Division
a) –8y = 17
b) 3.2x = -16
c) –x = 25
Now You Try It! - Solve the equation. Check your solution.
Check!
x
1)
14 =
8
2)
3)
x
4.5
= 12
56 = –3.5x
2
4)
8x = 72
5)
–y = 20
EXAMPLE 3 - Writing and Solving an Equation
Pizza Three people equally share the cost of a pizza. The total cost of the pizza is $14.67. Write and
solve an equation to find each person’s cost.
Solution
Let c represent each person’s cost.
Number
= of people

Think: what part
of the verbal
model is missing?
What values
correspond to each
part of the verbal
model?
3