Name: _______________________________________
Honors Algebra 1 Unit 1
Solving Linear Equations
What’s My Number?
ACTIVITY 2 PRACTICE
Answer each item. Show your work.
Lesson 2 – 1
1) Which of the following shows the Addition Property of Equality?
b. 16 2
a.
16 2.5
c. 8 2 d. 4 3 10
12 2
20
8
1 4
8
18
2
Solve each equation.
2) 3 3)
5 4) 4 2
13
10
5
60
2 2
5)
3
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6) Which equation has the solution
a. 2
c.
4
4
4?
16
3
7) Is 7 a solution of 5
3
b. 3
6
d.
6 3
2
2
6
12? Justify your answer.
8) The perimeter of triangle ABC is 54 inches. Find the length of each side.
A group of 19 students want to see the show at the planetarium. Tickets cost $11 for each student who is a
member of the planetarium’s frequent visitor program and $13 for each student who is not a member. The total
cost of the students’ tickets is $209.
Use this information for Items 9–12.
9) Let x represent the number of students in the group who are members of the frequent visitor program. Write
an expression in terms of x for the number of students in the group who are not members.
10) Write an equation to determine the value of x. Explain what each part of your equation represents.
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11) Solve the equation you wrote in Item 10. List a property of equality or provide an explanation for each step.
12) How many students in the group are members of the frequent visitor program? How many are not
members? Explain how you know.
Lesson 2 – 2
13) 6
2 6 3 4
14) 3 2 15) 5 2 1 9 4
6 3 4
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16) 2
3 4
5 2
4
17) Which equation has the greatest solution?
a.
0.4 2.5 1.3 4.7
c.
5
b.
2.4 d.
9
6 5.6 8
3
18) Provide a reason for each step in solving the equation shown below.
2(x − 1) − 3(x + 2) = 8 − 4x
2x − 2 − 3x − 6 = 8 − 4x
−1x − 8 = 8 − 4x
−1x + 4x − 8 = 8 − 4x + 4x
3x − 8 = 8
3x − 8 + 8 = 8 + 8
3x = 16
3
3
16
3
1
5
3
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19) Tyrell exercised this week both by walking and by biking. He walked at a rate of 4 mi/h and biked at a rate
of 12 mi/h. The total distance he covered both walking and biking was 36 miles, and Tyrell spent one more
hour walking than biking.
a. Define a variable and write an equation for this situation.
b. How many hours did Tyrell spend on each activity?
Lesson 2 – 3
Tickets to the planetarium cost $11 for members of the planetarium's frequent visitor program and $13 for
visitors who are not members of this program. Joining the frequent visitor program at the planetarium costs $5
per year.
Use this information for Items 20–23.
20) Write an equation that can be used to determine n, the number of visits per year for which the cost of being
a member of the frequent visitor program is equal to the cost of not being a member.
21) Solve your equation from Item 20. List a property of equality or provide an explanation for each step.
22) Explain the meaning of the solution of the equation.
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23) Nash plans to visit the planetarium twice in the next year. Should he join the frequent visitor program?
Explain.
For Items 24–27, solve the equation. Explain each step.
24) 8 5
25) 3 11
26) 6 9
27) 0.5 3 15
2 – 5
8 3.5
11
0.2 0.5
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Lesson 2 – 4
Solve each equation. If an equation has no solutions, or if an equation has infinitely many solutions,
explain how you know.
28) 3 29) 4 2 30) 6 31) 0.3 32) 6 4 6 8 1.8
2 4
2 5 5
2 2 4
2
5 0.4 4 2 5 8 7
0.2
2 8
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33)
1
MATHEMATICAL PRACTICES
Construct Viable Arguments and Critique the Reasoning of Others
A student solved the equation 2 4 4 6 9 4 as shown below. Did the student solve the
equation correctly? If so, list a property or explanation for each step. If not, solve the equation correctly, and list
a property or explanation for each step.
4 4 6 9 4
8 4 6 9 4
2 8 3 4
2 2 8 3 2 4
8 5 4
8 4 5 4– 4
12 5
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