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Mathematics 8
Items to Support Formative Assessment
Unit 3: Analyzing Functions and Equations
8.EE.C.7 Solve linear equations in one variable.
8.EE.C.7a Give examples of linear equations in one variable with one solution, infinitely
many solutions, or no solutions. Show which of these possibilities is the case by successively
transforming the given equation into simpler forms, until an equivalent equation of the
form x = a, a = a, or a = b results (where a and b are different numbers).
8.EE.C.7a (Short Item) Given the equation, determine if the solution is “Always true”,
“Sometimes true”, or “Never true”. Show your work and explain why.
1. x - 3 = 3 + x
2. 10x = x
3. 2x (15) = 30x
Possible answers:
1. x – 3 = 3 + x
x–x–3=3+x–x
-3=3
not true; Never true
There is never a number that will make this equation true.
2. 10x = x
10x – x = x – x
9x = 0
divide by 9 on both sides
Sometimes true; this equation is only true when x = 0. When x = any other number then it isn’t
true!
3. 2x(15)=30x
multiply 2(15)
divide by 30 on both sides
Always true; this equation is always true for x. When x= any number it is true on both sides of
the equation.
8.EE.C.7 Solve linear equations in one variable.
8.EE.C.7b Solve linear equations with rational number coefficients, including equations
whose solutions require expanding expressions using the distributive property and
collecting like terms.
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8.EE.C.7b
Leslie is considering the expressions 5( x + 2) - 6 and - (3x + 9) + 2(4 x + 8) . She wants to know if
one expression is greater than the other for all values of x.
1. Which statement about the relationship between the expressions is true?
a. The value of the expression 5( x + 2) - 6 is always equal to the value of the expression
-(3x + 9) + 2(4 x + 8).
b. The value of the expression 5( x + 2) - 6 is always less than the value of the expression
-(3x + 9) + 2(4 x + 8).
c. The value of the expression 5( x + 2) - 6 is always greater than the value of the expression
-(3x + 9) + 2(4 x + 8).
d. The value of the expression 5( x + 2) - 6 is always sometimes greater than and sometimes less
than value of the expression -(3x + 9) + 2(4 x + 8).
2. Explain how you found your answer to question #1.
3. Write a new expression that always has a greater value than both of these expressions.
Solutions:
1. b
5( x + 2) - 6
5x +10 - 6
5x - 4
2. and
-(3x + 9) + 2(4 x + 8)
-3x - 9 + 8x +16
5x + 7
When I simplified the expressions, I noticed that 5x +7 would always have a greater value than
the expression 5x-4 because it has a greater y-intercept even though the slopes are the same.
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under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.
3. Possible Solution: -5(-x+12)
8.EE.C.7a&b (Short item)
Part 1: Solve the equation for b.
1
-3(4b -10) = (-24b + 60)
2
Part II:
Select the statement that correctly interprets the solution to the equation in part I:
a.
b.
c.
d.
There is no solution
The solution is b=0
There are infinite solutions
It can only be solved when b = -12
Solution:
Part I:
1
-3(4b -10) = (-24b + 60)
2
-12b + 30 = -12b + 30
30 = 30
Part II: C
8.EE.C.7b Short Task
McKala wants to buy a pair of boots. She goes to the mall and sees that Shoe World has the
boots on sale for $25 off the original price. She is ready to purchase the boots when Jasmine
informs McKala that next door at Shoe Parade the same boots are on sale for 40% off the
original price. For what original price will these discounts be equal, if ever? Explain your
reasoning.
Let x = original price
Store A:
x - 25 = .60x
Store B
Setting up the equations and setting them equal to each other we find x - 25 = 0.60x. Like terms
on like sides, we have x - 0.60x = 25. Simplify: 0.4x = 25. Divide both sides by 0.40. x =
$62.50. There is one price for the boots when they are equal in price at both stores.
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under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.
8.EE.C.7ab (Short item)
Classify each equation as having one solution, no solution, or infinitely many solutions by
placing a check mark in the appropriate column.
No solutions
One solution
Infinitely many
solutions
No solutions
One solution
Infinitely many
solutions
2(x +1)+ 3x = 2x +1
2.2x + 6 -.07x = -0.5x + 2(x + 3)
-4x +18 = 2(6x + 9)
Solution:
2(x +1)+ 3x = 2x +1

2.2x + 6 -.07x = -0.5x + 2(x + 3)

-4x +18 = 2(6x + 9)
5(x + 2) - 2 = 9x - 3- 4x


Howard County Public Schools Office of Secondary Mathematics Curricular Projects has licensed this product
under a Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License.