Download Lesson 4: Solving Multiplication Equations Example 1 Example 2

Unit 1: Solving Equations
Lesson 4: Solving Multiplication Equations
In order to solve multiplication equations, we will use the opposite operation: ________________
Example 1
Example 3
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Example 2
A Few Notes About Fractions:
Example 4
Unit 1: Solving Equations
Lesson 4: Solving Multiplication Equations
Directions: Solve each equation on your own paper. If your answer is a decimal, round to the
nearest hundredth.
1. 10x = 80
2. -12x = 36
3. -9x = - 81
4. -2x = 17
5. .5x = 1.2
6. -4.4x = -9.2
7. -2/3x = 109
8. 4/7x = -6/7
9. -8/9x = 16
10. .8y = 8
11. ¾ = -2/3x
12. 1/2x = 5.5
13. -19 = -3j
14. 14k = -45
15. 9.3p = 82.1
16. -6/7 = 3/7a
BONUS:
17. 140 people registered for a volleyball tournament. How many 6 person teams can be formed?
Number of people on a team • Number of teams = Total number of registrants
6
•
t
6t = 140
=
140
(Solve for t)
18. John makes $12.45 an hour at his part-time job. Last week he made $174.30. How many
hours did John work?
Pay rate • Number of hours worked = Total Pay check
Copyright© 2009 Algebra-class.com
Unit 1: Solving Equations
Directions: Solve each equation. Show every step. (2 points each)
1. -6r = 84
2. -2/3x = -14
3. .7x = 8.4
4. 3/4y = -3/5
5. -135 = -9y
Copyright© 2009 Algebra-class.com
Unit 1: Solving Equations
Lesson 4: Solving Multiplication Equations
Answer Key
Directions: Solve each equation. If your answer is a decimal, round to the nearest hundredth.
1. 10x = 80
2. -12x = 36
10x = 80
10
10
2. -12x = 36
-12
-12
x=8
x = -3
3. -9x = - 81
4. -2x = 17
9x = - 81
-9
-9
-2x = 17
-2 -2
x=9
x = -17/2 or -8.5
5. .5x = 1.2
6. -4.4x = -9.2
5x = 1.2
.5
.5
-4.4x = -9.2
-4.4 -4.4
x = 2.4
x = 2.09
7. -2/3x = 109
∙
8. 4/7x = -6/7
= 109 ∙
x = -163.5
∙
= 16 ∙
∙
x = -3/2 or -1.5
9. -8/9x = 16
∙ = 10. .8y = 8
.8y = 8
.8
.8
x = -18
y = 10
Copyright© 2009 Algebra-class.com
Unit 1: Solving Equations
11. ¾ = -2/3x
12. 1/2x = 5.5
-2/3x = ¾
(2) 1/2x = 5.5(2)
(-3/2) -2/3x = ¾(-3/2)
x = 11
x = -9/8
13. -19 = -3j
14. 14k = -45
-3j = -19
-3
-3
14k = -45
14
14
j = 19/3
k = -45/14
15. 9.3p = 82.1
16. -6/7 = 3/7a
9.3p = 82.1
9.3
9.3
(7/3) 3/7a = -6/7 (7/3)
a = -2
p = 8.83
BONUS:
17. 140 people registered for a volleyball tournament. How many 6 person teams can be formed?
Number of people on a team • Number of teams = Total number of registrants
6
•
t
=
140
6t = 140
(Solve for t)
6t = 140
6
6
t = 23.3 (23 6 person teams can be formed.
18. John makes $12.45 an hour at his part-time job. Last week he made $174.30. How many
hours did John work?
Pay rate • Number of hours worked = Total Pay check
12.45 •
h
= 174.30
12.45h = 174.30
12.45
12.45
h = 14 (John worked 14 hours)
Copyright© 2009 Algebra-class.com
Unit 1: Solving Equations
1. -6r = 84
-6r/-6 = 84/-6
Divide by -6 on both sides
r = -14
Simplify: 84/-6 = -14
2. -2/3x = -14
(-3/2)-2/3x = -14(-3/2)
x = 21
Multiply both sides by (-3/2) (the reciprocal of 2/3
Simplify: -14(-3/2) = 21
3. .7x = 8.4
.7x/.7 = 8.4/.7
Divide both sides by .7
x = 12
Simplify: 8.4/.7
4. 3/4y = -3/5
(4/3)3/4y = -3/5(4/3)
Multiply by the reciprocal: 4/3 on both sides
y = -8/10
Simplify: (-3/5)(4/3) = -8/10
5. -135 = -9y
-135/-9 = 9y/-9
Divide both sides by -9
15 = y
Simplify: -135/-9 = 15
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Solving Equations
Lesson 4A: Writing and Solving Multiplication Equations
Example 1
A local college is sponsoring a volleyball tournament. 96 people signed up to play in the
tournament. How many 6 person teams can be formed?
Example 2- Distance Formula
D = rt
Julia drove at an average rate of 62 mph on her trip to the ocean. Her total distance was 375
miles. About how many hours did Julia drive?
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Solving Equations
Lesson 4A: Writing and Solving One-Step Multiplication Equations
Directions: Write a verbal model and an algebraic equation for each problem. Then solve.
1. Lori drove for 4.5 hours while on a business trip. She traveled at total of 306 miles. At what rate
did Lori travel?
2. Ashton must buy 18 gifts and he has a budget of $216. How much should each gift cost in order
for Ashton to meet his budget?
Over the course of a month, James earned $135 mowing 9 lawns. How
much did he charge per lawn?
Copyright© 2009-2014 Algebra-class.com
Solving Equations
Lesson 4A: Writing and Solving One-Step Addition Multiplication Answer Key
Directions: Write a verbal model and an algebraic equation for each problem. Then solve.
1. Lori drove for 4.5 hours while on a business trip. She traveled at total of 306 miles. At what rate
did Lori travel?
This problem can utilize the distance formula. Distance – rate(time)
D=rt
D = 306 miles
306 = r(4.5)
or
T = 4.5 hours
or
D=rt
R= ?
4.5r = 306
This is the equation
4.5/4.5r = 306/4.5
Divide both sides by 4.5
r = 68 miles/hour
Lori drove at a rate of 68 miles/hour.
2. Ashton must buy 18 gifts and he has a budget of $216. How much should each gift cost in order
for Ashton to meet his budget?
Let’s first write a verbal model and identify our variable.
18 gifts · ( price of gifts) = total budget of 216
Let x = cost of each gift
18x = 216
Equation
18/18x = 216/18
Divide by 18 on both sides
x = 12
Each gift should $12 in order for Ashton to meet his budget.
Over the course of a month, James earned $135 mowing 9 lawns. How
much did he charge per lawn?
Let’s first write a verbal model and identify our variable.
9 lawns · (charge per lawn) = total earned
Let x = amount charged per
lawn
9x = 135
Equation
9/9x = 135/9
Divide by 9 on both sides
x = 15
James charged $15 per lawn.
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