Name:
Infinitely Many and No Solutions Classwork (8EE7)
Warm-Up:
Solve the following equations.
1) 6(y – 2) = 2y + 12 2) -2(x + 4) = x – 5 + 3x
3) Which properties did you use to solve these problems?
A Magic Trick #1 (Pair-Share) a) Pick a number, any number with your partner. Fill in your number in the box b) Substitute your number into the equation below:
2y + 6 = ½ (4y + 12) c) Explain your solution in a sentence.
THE TRICK d) Pick a different number – maybe a negative integer, decimal or fraction.
Fill in your number in the box e) Substitute your number into the equation below:
2y + 6 = ½ (4y + 12) f) Explain your solution in a sentence.
Date:

Name: Date:
Around the World #1:
1) List the values which you see your classmates have chosen:
2) Analyze each of your classmate’s work, be careful to pay attention to each step completed in each equation.
Describe the pattern. Will this pattern continue if we choose even more numbers?
Definition of Infinitely Many Solutions:
In my own words this means,
______________________________________________________________________.
Practice: Solve the equation below.
-3(2x – 4) + 2 = -6x + 14
Check and make sure that the equation has infinitely many solutions.
-3(2x – 4) + 2 = -6x + 14

Name: Date:
A Second Magic Trick (Pair-Share) a) Pick a number, any number with your partner. Fill in your number in the box b) Substitute your number into the equation below:
3w – 10 + w = ¼ (12w – 40) c) Explain your solution in a sentence.
Around the World #2:
1) List the values which you see your classmates have chosen:
2) Analyze each of your classmate’s work, be careful to pay attention to each step completed in each equation.
Describe the pattern. Will this pattern continue if we choose even more numbers?
3) How is the pattern in this second Around the World different than the first?
Definition of No Solution:
In my own words this means, ______________________________________________________________________.

Name:
Practice: Solve the equation below.
-x + 12 – 4x = -5x + 1
Summary:
Look at the following equations.
What are the solutions to #1 and #2?
1) 4y + 12 = 4y – 7
Explain to your partner what each solution means.
-4y -4y
12 = -7
Answer: ____________________________________
2) 3(a – 2) = 3a – 6
3a – 6 = 3a – 6
Answer: ____________________________________
Graphic Organizer:
Date:

Name: Date:
Classwork: Solve the following equations. Some equations will have 1 solution, others will have no solution, and still others will have infinite solutions.
1) 3(x – 1) = 2x + 9 2) -2n + 5 = -2(n + 1)
3) 4(y – 1) = ½ (y – 8) 4) 4(2w + 1) = 5w + 3w + 9
5) 4a + 1 = 2(2a + 3) 6) 6x – 5 = 7x – 1
7) Cheerleaders are selling raffle tickets for a large screen TV in order to raise money for new
uniforms. The cheerleading coach made the following statements regarding ticket sales:

If you take the number of tickets Kate sold, add 12, multiply the sum by 8 and divide the product by 2, you will know the number of tickets Jamie sold.
Let x = the number of raffle tickets that Kate sold
Then, the number of raffle tickets that Jamie sold is 8(x+12)
2
 If you take the number of tickets Kate sold, subtract 8, multiply the sum by 6, and divide the product by 3, you will know the number of tickets Nikki sold.
Let x = the number of raffle tickets that Kate sold
Then, the number of raffle tickets that Jamie sold is 6(x - 8)
3

Name: Date: a.) Simplify the expression that represents the amount of tickets that Jamie sold. b.) Simplify the expression that represents the amount of tickets that Nikki sold. c.) Using your answers from part (a) and part (b), determine the amount of tickets Kate sold, if both
Jamie and Nikki sold the same amount of tickets. (Hint: set the two expressions equal to each other). d.) Is there one solution, no solution, or infinitely many solutions?
Assessment:
Mario solves the following equation. He has at least 1 mistake in his work. Can you help him fix his work?
-3(x + 4) = 2x – 5x + 4
3x + 12 = -3x + 4
+ 3x + 3x
12 = 4
This is false! There are infinitely many solutions