Download 1. Sam used the rules of solving equations to find the solution was x

1. Sam used the rules of solving equations to find the
solution was x = -7. Write at least 2 different problems
that might possibly have been the question asked by the
teacher that led Sam to the correct answer. Prove your
problems are valid responses by solving each equation.
2. Juan and five buddies attended the Captain America:
Civil War premier at Keystone Cinemas. They spent $97
total. They had purchased 5 bags of popcorn and 6 tickets.
What could be the prices of the tickets and popcorn in
order to reach the $97 total?
3. Look at the table below. Write a rule for the
multiplication rule of integers from what you can see in
the table?
5 x -3 = -15 -5 x -3 = 15
5 x -2 = -10 -5 x -2 = 10
5 x -1 = -5 -5 x -1 = 5
5x0 =0
-5 x 0 = 0
5x1 =5
-5 x 1 = -5
5 x 2 = 10 -5 x 2 = -10
5 x 3 =15 -5 x 3 =-15
5. Describe the pattern you see in the list of numbers
below:
13, 26, 39, 52, 65
4. If the pattern shown in the table continues, what
amount will have been raised by Week 5?
Scholarship Funds
Week
0
1
2
3
?
Amount
0
0
2
4
6
(thousands $)
7. Look at the original expression of 8 + 4 ∙ 2 + 6 ÷ 3.
Below are three expressions that have the same numbers
but the parentheses are in different places. Determine
which ones have the same answer as the original
expression and explain why they have the same answer.
a) 8 + (4 ∙ 2) + 6 ÷ 3
b) (8 + 4) ∙ 2 + 6 ÷ 3
c) 8 + 4 ∙ 2 + (6 ÷ 3)
8. Which equation represents the table shown?
Hours
Money ($)
15
127.50
25
212.50
35
297.50
9. Gemma said, “I found a way to decide if the difference
is positive or a negative when I subtract integers.” What
way do you think Gemma found?
10. Find two integers that when subtracted have a
negative number as the difference. How can you come up
with more integer pairs that fit the description?
11. Create an equation that has solution of x = 5. Use
more than one operation.
12. Write two rational expressions whose product is 1.
13. Create a geometry problem using multiplication of
rational expressions to find an expression for the area of a
triangle. Then solve that problem.
14. Use a property other than a product of powers to
write an expression that is equivalent to 16x8.
15. Use a whole number other than 1 and a fraction to get
a product less than 1.
16. Add 458 and 397 in two different ways. How are the
ways you added them alike? How are they different?
17. How can you solve this equation in more than one
way?
4(𝑥 + 3) − 6
−8=7
3
18. Tobin subtracted two integers. His difference was -12.
Find 3 pairs of numbers that he could have subtracted.
19. Divide 8/9 by 2/3 using two different methods. How are
the methods you used to divide them alike? How are they
different?
20. The area of a rectangle is x2 – x – 2, find a length and
width.
6. Find 2 fractions whose quotient is 2 2/3.
a. y = 8.5x
c. y = 15x
b. y = 8.5x + 12.50
d. y = 15x + 12.50