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Know it for Alg 1
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Copyright © by Holt, Rinehart and Winston. 31 Algebra 1All rights reserved.
2-1 Solving One-Step Equations
Solve each equation.
1. a � 45 � 36 2. 5 � b � 0.65 3. 5a � 25 4. ��13�c � ��
23�
5. Gary had $231. After he bought a video game, he had $186. Write and solvean equation to find the amount of money Gary spent on the video game.
2-2 Solving Two-Step Equations
Solve each equation.
6. �2a � 8 � 14 7. 8.5b � 6 � 53.5 8. 9 � �14�c � �
38� 9. 5d � 24 � �36
10. A car can be rented for $45 plus $0.14 per mile. Tammy paid $63.90. Writeand solve an equation to show how many miles Tammy drove.
2-3 Solving Multi-Step Equations
Solve each equation. Check your answer.
11. �d �
47
� � 3 12. 5h � 7 � h � 5
13. 3(p � 2) � 18 14. �9k
4� 7� � 5
15. Marty organized his CDs onto 4 shelves. The top shelf holds 3 CDs, thesecond shelf holds 6, and the 2 bottom shelves hold the same number ofCDs. Marty has a total of 19 CDs. How many CDs does the bottom shelfhold?
Chapter Review2
CHAPTER
Copyright © by Holt, Rinehart and Winston. 31 Algebra 1All rights reserved.
2-1 Solving One-Step Equations
Solve each equation.
1. a � 45 � 36 2. 5 � b � 0.65 3. 5a � 25 4. ��13�c � ��
23�
5. Gary had $231. After he bought a video game, he had $186. Write and solvean equation to find the amount of money Gary spent on the video game.
2-2 Solving Two-Step Equations
Solve each equation.
6. �2a � 8 � 14 7. 8.5b � 6 � 53.5 8. 9 � �14�c � �
38� 9. 5d � 24 � �36
10. A car can be rented for $45 plus $0.14 per mile. Tammy paid $63.90. Writeand solve an equation to show how many miles Tammy drove.
2-3 Solving Multi-Step Equations
Solve each equation. Check your answer.
11. �d �
47
� � 3 12. 5h � 7 � h � 5
13. 3(p � 2) � 18 14. �9k
4� 7� � 5
15. Marty organized his CDs onto 4 shelves. The top shelf holds 3 CDs, thesecond shelf holds 6, and the 2 bottom shelves hold the same number ofCDs. Marty has a total of 19 CDs. How many CDs does the bottom shelfhold?
5
38
25
45 � 0.14x � 63.90; 135 miles
�12�629�7�3
186 � v � 231; $45
254.35�9
Chapter Review2
CHAPTER
Copyright © by Holt, Rinehart and Winston. 32 Algebra 1All rights reserved.
2-4 Solving Equations with Variables on Both Sides
Solve each equation. Check your answer.
16. a � 15 � �4a 17. 0.45b � 2.25b � 9 18. �35�c � �
15� � �1
10�c 19. �2d � 14 � �4 � d
2-5 Solving Proportions
Solve each proportion.
20. �6d� � �1
26� 21. �5
t� � �
2250� 22. �
01..55� � �m
2�.50.5�
23. A hummingbird’s heart beats 1263 beats per minute. Find the unit rate in beats per second. Round to the nearest hundredth.
2-6 Solving Literal Equations for a Variable
24. Solve p � 4 � m for m. 25. Solve ab � 8 � c for a.
26. Solve mn � 3 � s for n. 27. Solve �d �f
5� � g for f.
28. The formula for the perimeter of a rectangle is P � 2l � 2w, where l is the length and w is the width. Solve for w.
2-7 Solving Absolute-Value Equations
Solve each equation.
29. 9 � �x � 4� 30. 5�x � 5� � 10 � 7
31. �x � 3� � 8 � 2 32. �x � 50.37� � 22.07
33. In the winter Bruce keeps his room thermostat set at 67°F to conserve energy.The thermostat controls the furnace so that the room temperature stays within 3°of this setting. Write and solve an equation to find the minimum and maximumtemperatures in the Bruce’s room.
CHAPTER 2 REVIEW CONTINUED
Copyright © by Holt, Rinehart and Winston. 32 Algebra 1All rights reserved.
2-4 Solving Equations with Variables on Both Sides
Solve each equation. Check your answer.
16. a � 15 � �4a 17. 0.45b � 2.25b � 9 18. �35�c � �
15� � �1
10�c 19. �2d � 14 � �4 � d
2-5 Solving Proportions
Solve each proportion.
20. �6d� � �1
26� 21. �5
t� � �
2250� 22. �
01..55� � �m
2�.50.5�
23. A hummingbird’s heart beats 1263 beats per minute. Find the unit rate in beats per second. Round to the nearest hundredth.
2-6 Solving Literal Equations for a Variable
24. Solve p � 4 � m for m. 25. Solve ab � 8 � c for a.
26. Solve mn � 3 � s for n. 27. Solve �d �f
5� � g for f.
28. The formula for the perimeter of a rectangle is P � 2l � 2w, where l is the length and w is the width. Solve for w.
2-7 Solving Absolute-Value Equations
Solve each equation.
29. 9 � �x � 4� 30. 5�x � 5� � 10 � 7
31. �x � 3� � 8 � 2 32. �x � 50.37� � 22.07
33. In the winter Bruce keeps his room thermostat set at 67°F to conserve energy.The thermostat controls the furnace so that the room temperature stays within 3°of this setting. Write and solve an equation to find the minimum and maximumtemperatures in the Bruce’s room.
�x � 67� � 3; 64°F; 70°F
28.3; 72.44�7; 13
�13; 5
w � �P �
22l
�
f � �d �
g5
�n � �s
m� 3�
a � �8 �b
c�m � �p � 4
21.05 beats/sec
86.2548
��130��
25�5�3
CHAPTER 2 REVIEW CONTINUED
Copyright © by Holt, Rinehart and Winston. 33 Algebra 1All rights reserved.
Answer these questions to summarize the important concepts fromChapter 2 in your own words.
1. Explain how the four properties of equality help you solve equations.
2. Explain how you can solve a proportion for a missing value.
3. What are the steps for solving a literal equation for a variable?
4. Explain why an absolute-value equation may not have two solutions.
For more review of Chapter 2:
• Complete the Chapter 2 Study Guide and Review on pages 122–125 ofyour textbook.
• Complete the Ready to Go On quizzes on pages 101 and 121 of yourtextbook.
Big Ideas2
CHAPTER
Copyright © by Holt, Rinehart and Winston. 33 Algebra 1All rights reserved.
Answer these questions to summarize the important concepts fromChapter 2 in your own words.
1. Explain how the four properties of equality help you solve equations.
2. Explain how you can solve a proportion for a missing value.
3. What are the steps for solving a literal equation for a variable?
4. Explain why an absolute-value equation may not have two solutions.
For more review of Chapter 2:
• Complete the Chapter 2 Study Guide and Review on pages 122–125 ofyour textbook.
• Complete the Ready to Go On quizzes on pages 101 and 121 of yourtextbook.
An absolute-value equation that simplifies to an absolute-valueequaling a negative number, has no solutions. An absolute-valueequation that simplifies to an absolute-value equaling 0, has onlyone solution.
Step 1 Locate the variable you are asked to solve for in theequation.
Step 2 Identify the operations on this variable and the order inwhich they are applied.
Step 3 Use inverse operations to undo operations and isolate thevariable.
You can solve proportions for a missing value by using the CrossProducts Property, which states that in a proportion, crossproducts are equal. Then solve the equation for the missing value.
When adding, subtracting, multiplying, or dividing the samenonzero number on both sides of an equation, the statement willstill be true.
Big Ideas2
CHAPTER
