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```CCSS Grade 8
Unit 3: Equations with One Variable
Study Guide
Name ___________________________
Class _______________ Period _______
Date ____________________________
Read all instructions carefully before you begin. Be sure your answers are complete and include all the
information required (work shown with units, justification, etc.).
1.
What is the possible result of simplifying
the equation 20x – 2 = 2 (10x – 2)? Show
a) -2 = -2
b) x = 2
c) -2 = -4
d) x = 0
e) 20x – 2 = 20x – 4
f) 2 = 0
2.
Suppose a linear equation with one
variable, x, is simplified. Circle the letter(s)
of the following resulting equations that
would indicate that the original equation
has no solution? Explain your reasoning.
(10points) (8.EE.7)
a) -3 = 3
b) 1 = x
c) 1 = 1
d) x = -8
e) 1 = -1
f) x = x
3.
Determine the number of solutions that each equation has by writing a check mark (√) on the □. Show
a)
2(3c + 6 – 4c) = 8
□ One Solution □ No Solutions □ Infinitely many solutions
b)
2x  2 2x  4

14
6
□ One Solution □ No Solutions □ Infinitely many solutions
c)
9p+3p–10 = 3(3p + p)
□ One Solution □ No Solutions □ Infinitely many solutions
d)
3
1
(4 f  10)  f  (2 f  2) □ One Solution □ No Solutions □ Infinitely many solutions
2
2
e)
9 + m = 2m + 9
□ One Solution □ No Solutions □ Infinitely many solutions
f)
18h – 5 = 3(6h – 5)
□ One Solution □ No Solutions □ Infinitely many solutions
2(3c + 6 – 4c) = 8
3
1
(4 f  10)  f  (2 f  2)
2
2
2x  2 2x  4

14
6
9 + m = 2m + 9
9p + 3p – 10 = 3(3p + p)
18h – 5 = 3(6h – 5)
4.
Select numbers from below for the missing value that will create an equation with the indicated
number of solutions. (5 points each; 15 points total) (8. EE.7) Show your work below to make sure that
it satisfies the condition.
0
1
2
3
4
5
6
7
8
9
Equation with no solution
7x – 2x + 5 – x = ____ x + ____
Equation with one solution
7x – 2x + 5 – x = ____x + ____
Equation with infinitely many solutions
7x – 2x + 5 – x = _____x + _____
Solve the Equation you created above with No
Solution (5 points):
Solve the Equation you created above with one
solution (5 points):
Solve the Equation you created above with infinitely many solutions (5 points):
5a.
How many solutions are there to 8x – 7 = 2(2x + 7) – 5? Show your work and explain your reasoning. (5
points) (8. EE.7)
5b.
Change one number in your equation in part b so that the number of solutions for the new equation
differs from the equation in part a. How many solutions does your equation have? Show your work,
and explain your reasoning. (5 points) (8. EE.7)
5c.
Change one number in your equation in part b so the number of solutions for the new equation differs
from the equations in parts a and b. How many solutions does this equation have? Show your work
and explain your reasoning. (5 points) (8. EE.7)
6.
Sarah solve the equation –x + 5(x + 6) = 4x + 30 as shown, and concluded that there is no solution. Do you agree
or disagree with her? Explain your reasoning and show your work. (5 points) (8. EE.7)
-x + 5(x + 6) = 4x + 30
-x + 5x + 6 = 4x + 30
4x – 4x + 6 = 4x – 4x + 30
6 = 30
7.
A planter box has the following dimensions. The perimeter is 58 inches. Write an equation to find the
unknown value. Then calculate the expected length and width. (5 points) (8. EE.7)
8.
Andy’s Rental Car charges an initial fee of \$20 plus an additional \$30 per day to rent a car. Buddy’s
rental Car Charges an initial fee of \$36 plus an additional \$28 per day. For what number of days is the
total cost charged by the companies the same? (5 points) (8. EE.7)
9.
Country carpets charge\$22 per square yard for carpeting, and an additional installation fee of \$100.
City carpets charges \$25 per square yard for the same carpet, plus an additional installation fee of \$70.
Find the number of square yards of carpeting for which the cost would be the same for both stores. (5
points) (8. EE.7)
```