Learn to solve equations using multiplication and division'

1
Learn to solve equations using multiplication and
division.
2
Vocabulary
Division Property of Equality Multiplication
Property of Equality
3
You can solve a multiplication equation using the
Division Property of Equality.
You can divide both sides of an equation by the
same nonzero number, and the equation will still
be true.
4 3 12
x y
4 3 12
x y
2
2
z
z
4
Additional Example 1 Solving Equations Using
Division
Solve 8x 32.
8x 32
Divide both sides by 8.
8x 32
8
8
1x 4
1 x x
x 4
Check
8x 32
Substitute 4 for x.
?
5
Try This Example 1
Solve 9x 36.
9x 36
Divide both sides by 9.
9x 36
9
9
1x 4
1 x x
x 4
Check
9x 36
Substitute 4 for x.
?
6
You can solve a division equation using the
Multiplication Property of Equality.
You can multiply both sides of an equation by the
same number, and the statement will still be true.
2 3 6
x y
2 3 6
x y
8 3 24
7
Additional Example 2 Solving Equations Using
Multiplication
Solve 7.
7
7
Multiply both sides by 7.
n 49
Check
Substitute 49 for n.
?
8
Try This Example 2
Solve 16
4
4
Multiply both sides by 4.
n 64
Check
Substitute 64 for n.
?
9
Sometimes it is necessary to solve equations by
using two inverse operations. For instance, the
equation 6x ? 2 10 has multiplication and
subtraction.
Variable term
6x ? 2 10
Multiplication
Subtraction
To solve this equation, add to isolate the term
with the variable in it. Then divide to solve.
10
Additional Example 5 Solving a Simple Two-Step
Equation
Solve 3y 7 20.
Add 7 to both sides to isolate the term with y in
it.
3y 7 20
Step 1
7
7
3y 27
Step 2
3y 27
Divide both sides by 3.
3
3
y 9
11
Try This Example 5
Solve 4y 5 29.
Subtract 5 from both sides to isolate the term
with y in it.
4y 5 29
Step 1
5
5
4y 24
Step 2
4y 24
Divide both sides by 4.
4
4
y 6
12
Additional Example 4 Solving Algebraic
Expressions by Combining Like Terms
Solve x 3x 48.
x 3x 48
Identify like terms. The coefficient of x is 1.
4x 48
Combine coefficients 1 3 4
4x 48
Divide both sides by 4.
4
4
x 12
13
Try This Example 4
Solve 7c c 102.
7c c 102
Identify like terms. The coefficient of c is 1.
Combine coefficients 7 1 6
6c 102
6c 102
Divide both sides by 6.
6
6
c 17
14
Lesson Quiz
Solve. 1. 3 2. 16t 112 3. 14 4.
3n 17 29 5. Joan is making a scrapbook of
her pictures. She wants to put three pictures on
each page. She has 63 photos. Write and solve an
equation to find how many pages she will need for
all of the photos.
k 18
t 7
b 126
n 4
21 pages
6. 6y y 42
y 6