Answers2025-2026_MDCPS_1205070-MJ Grade 8 Pre-Algebra Sem 1-CRUnit Test

Solving Equations with Rational Numbers Answers

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Paolo is putting a fence around his pool. The length of the pool is 20 feet, the width is feet, and the area of the pool is 300 square feet. Recall that area is length multiplied by width. The equation below models the area of the pool. What is the value of x? Round to the units place.

Question illustration
A
5
B
8
C
15
D
35
2
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Sanjay solved the equation below. Which property did he use to determine that is equivalent to ?

Question illustration
A
distributive property of equality
B
subtraction property of equality
C
multiplication property of equality
D
division property of equality
3

Solve the equation using the distributive property and properties of equality.What is the value of x?

Question illustration
A
6
B
7 and one-half
Option B
C
14 and one-half
Option C
D
30
Option D
4

What is the value of x in the equation below?

Question illustration
A
12
B
15
C
20
D
24
5

Consider the equation and its solution.What number should be in the empty box?

Question illustration
A
Negative 30
Option A
B
Negative 2
Option B
C
2
D
30
6

Which table shows the correct methods used to justify the solution steps?

Question illustration
A
A 2-column table with 4 rows. Column 1 is labeled Solution step with entries 3 x minus 15 + 7 x = 65, 10 x minus 15 = 65, 10 x = 80, x = 8. Column 2 is labeled Method to Justify with entries division property of equality, combine like terms, distributive property, addition property of equality.
Option A
B
A 2-column table with 4 rows. Column 1 is labeled Solution step with entries 3 x minus 15 + 7 x = 65, 10 x minus 15 = 65, 10 x = 80, x = 8. Column 2 is labeled Method to Justify with entries distributive property, combine like terms, addition property of equality, division property of equality.
Option B
C
A 2-column table with 4 rows. Column 1 is labeled Solution step with entries 3 x minus 15 + 7 x = 65, 10 x minus 15 = 65, 10 x = 80, x = 8. Column 2 is labeled Method to Justify with entries distributive property, addition property of equality, combine like terms division property of equality.
Option C
D
A 2-column table with 4 rows. Column 1 is labeled Solution step with entries 3 x minus 15 + 7 x = 65, 10 x minus 15 = 65, 10 x = 80, x = 8. Column 2 is labeled Method to Justify with entries division property of equality, combine like terms, addition property of equality, distributive property.
Option D
7

Noa hopes to pick the winning ticket during her math class’s raffle. The student who picks the ticket with a true statement will win. Which is the winning ticket?

A
4 (x minus 5) = 35 is equivalent to 4 x = 40
Option A
B
.
Option B
C
2 (x minus 6) = negative 35 is equivalent to 2 x = negative 23
Option C
D
9 (x minus 6) = negative 35 is equivalent to 9 x = negative 29
Option D
8

Henry showed all the steps he took to solve the equation. StepSimplified Expression1-234Sammy tried to verify the solution by substituting back into the original equation. It did not result in a true statement. Which explains why Henry’s solution is incorrect?

Question illustration
A
Step 1 is wrong because the distributive property of equality was used incorrectly.
B
Step 2 is wrong because the addition property of equality was used incorrectly.
C
Step 3 is wrong because the subtraction property of equality was used incorrectly.
D
Step 4 is wrong because the division property was used incorrectly.
9

Maria solved the equation. What methods did she use and in what order did she use them?

Question illustration
A
combining like termsdistributive propertyaddition property of equalitydivision property of equality
B
distributive propertyaddition property of equalitysubtraction property of equalitydivision property of equality
C
distributive propertycombining like termsaddition property of equalitydivision property of equality
D
distributive property of equalityaddition property of equalitycombining like termsdivision property of equality
10

Consider the equation and its solution.Which property is used in the last step to find that ?

Question illustration
A
distributive property
B
addition property of equality
C
subtraction property of equality
D
division property of equality

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