AnswersTX-College Prep Math BUnit Test

Solving Multi-Step Equations Answers

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1
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Celia uses the steps below to solve the equation .Step 1Distribute over the expression in parentheses.Step 2Simplify like terms.Step 3Subtract 3 from both sides of the equation.Step 4Divide both sides of the equation by –14.Which corrects the error in the step in which Celia made the first error?

Question illustration
A
In step 1, she should have also distributed over 2d, to get .
Option A
B
In step 1, she should have also distributed over –16d, to get .
Option B
C
In step 3, she should have added 3 to both sides of the equation to get .
Option C
D
In step 3, she should have first divided both sides by –14 to get .
Option D
2
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What is the value of x in the equation?

Question illustration
A
–36
B
–33
C
–24
D
Negative 18
Option D
3

Mr. Reddick has 74 total yards of red and blue felt to distribute to students in his art class. Each of his 20 students gets 2.5 yards of blue felt for the project. He also gives each student an equal amount of red felt. How much red felt does each student get?

A
1.2 yd
B
3.7 yd
C
12 yd
D
24 yd
4

A group of 8 friends went to lunch and spent a total of $76, which included the food bill and a tip of $16. They decided to split the bill and tip evenly among themselves. Which equations and solutions describe the situation? Select two options.

A
The equation represents the situation, where x is the food bill.
Option A
B
The equation represents the situation, where x is the food bill.
Option B
C
The solution represents the total food bill.
Option C
D
The solution represents each friend’s share of the food bill and tip.
Option D
E
The equation represents the situation, where x is the food bill.
Option E
7

The Schwartz family spent a total of $111.75 for Internet service for 3 months. Eachmonth they received $5.50 as a credit on the bill. Which equation and solution showsthe cost of their monthly Internet service before the credit?

A
; the monthly Internet service is $31.75
Option A
B
; the monthly Internet service is $42.75
Option B
C
; the monthly Internet service is $42.75
Option C
D
; the monthly Internet service is $31.75
Option D
8

Gisele trains 7 days per week for a biathlon. She covers a total of 20 miles cycling and running each day. Gisele cycles a total of 105 miles each week, and runs a certain number of miles per week. If she cycles the same number of miles each day and runs the same number of miles each day, the equation represents the situation. Which describes the solution, , to this equation?

Question illustration
A
The solution is 5, which represents the number of miles she runs each day.
B
The solution is 5, which represents the number of miles she runs each week.
C
The solution is 35, which represents the number of miles she runs each day.
D
The solution is 35, which represents the number of miles she runs each week.
9

What is the value of r in the equation?

Question illustration
A
–6
B
–4
C
4
D
6
10

A group of 4 friends went to lunch and spent a total of $40, which included the $34 food bill and the tip. They decided to split the bill and tip evenly among themselves.One of the friends used the equation to represent the situation, where t represents the total amount of the tip. Which describes the amount each friend paid for the food and for the tip?

Question illustration
A
Each friend paid $8.50 for the food and $1.50 for the tip.
B
Each friend paid $10.00 for the food and $6.00 for the tip.
C
Each friend paid $8.50 for the food and $6.00 for the tip.
D
Each friend paid $10.00 for the food and $1.50 for the tip.
11

A company is making new soccer uniforms for a team. The company uses 2.5 yards of fabric for each shirt. The company uses 82.5 yards of fabric to make shirts and shorts for 15 players. The equation and solution below represents the situation.What does the solution, , represent?

Question illustration
A
the total fabric needed for the shirts
B
the total fabric for each shirt and each pair of shorts
C
the amount of fabric left over after making the shirts and shorts
D
the amount of fabric needed for each pair of shorts
12

Hannah spends $4.50 each day to buy lunch at her school. After school each day, she buys the same snack. Hannah spends $28.75 for lunch and snacks each week. The equation and solution model the situation.; What does the solution, , represent?

Question illustration
A
the total cost of snacks for the week
B
the cost of each snack
C
the total amount of lunch for the week
D
the amount she spends each day for lunch and snack
13

Shawna, Dexter, and Tilana are solving the equation .Shawna says, “I can begin by dividing each side of the equation by –2.5 to get .”Dexter says, “I can begin by distributing to get .”Tilana says, “I can begin by multiplying each side of the equation by to get .”Which students are correct?

Question illustration
A
only Shawna and Tilana
B
only Shawna and Dexter
C
only Dexter and Tilana
D
Shawna, Dexter, and Tilana

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