Solving Equations by Multiplying or Dividing

1
Solving Equations by Multiplying or Dividing
1-8
Warm Up
Problem of the Day
Lesson Presentation
Course 3
2
Warm Up Write an algebraic expression for each
word phrase. 1. A number x decreased by 9 2. 5
times the sum of p and 6 3. 2 plus the product
of 8 and n 4. the quotient of 4 and a number
c
x 9
5(p 6)
2 8n
3
Problem of the Day How many pieces do you have
if you cut a log into six pieces and then cut
each piece into 4 pieces?
24
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Learn to solve equations using multiplication and
division.
5
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
Course 3
6
Additional Example 1A Solving Equations Using
Division
Solve 6x 48.
6x 48
Divide both sides by 6.
6x 48
6
6
1x 6
1 x x
x 8
Check
6x 48
Substitute 8 for x.
?
7
Additional Example 1B Solving Equations Using
Division
Solve 9y 45.
9y 45
Divide both sides by 9.
9y 45
9
9
1y 5
1 y y
y 5
Check
9y 45
Substitute 5 for y.
?
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Check It Out Example 1A
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.
?
9
Check It Out Example 1B
Solve 3y 36.
3y 36
Divide both sides by 3.
3y 36
3
3
1y 12
1 y y
y 12
Check
3y 36
Substitute 12 for y.
?
10
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
Course 3
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Additional Example 2 Solving Equations Using
Multiplication
Solve 5.
4
4
Multiply both sides by 4.
b 20
Check
Substitute 20 for b.
?
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Check It Out Example 2
Solve 5.
3
3
Multiply both sides by 3.
c 15
Check
Substitute 15 for c.
?
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Additional Example 3 Money Application
To go on a school trip, Helene has raised 670,
which is one-fourth of the amount she needs. What
is the total amount needed?
fraction of amount raised so far
amount raised so far
total amount needed
?



x
670
Write the equation.
Multiply both sides by 4.
4
4
x 2680
Helene needs 2680 total.
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Check It Out Example 3
The school library needs money to complete a new
collection. So far, the library has raised 750,
which is only one-eighth of what they need. What
is the total amount needed?
amount raised so far
total amount needed

?


x
750
Write the equation.
8
Multiply both sides by 8.
8
x 6000
The library needs to raise a total of 6000.
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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.
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Additional Example 4 Solving a Simple Two-Step
Equation
Solve 3x 2 14.
Subtract 2 to both sides to isolate the term with
x in it.
3x 2 14
Step 1
2
2
3x 12
Step 2
3x 12
Divide both sides by 3.
3
3
x 4
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Check It Out Example 4
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
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Lesson Quiz
Solve. 1. 3t 9 2. 15 3b 3. 7 4. z
4 22 5. A roller coaster descends a hill at a
rate of 80 feet per second. The bottom of the
hill is 400 feet from the top. How long will it
take the coaster rides to reach the bottom?
t 3
b 5
x 28
z 88
5 seconds