(7) Lesson 5.1 - Solve Equations with Rational Coefficients

1. Divide. Write in simplest form.
1. 2.
3. 4.
5. In 3 hours, the temperature dropped degrees. On
average, how many degrees did the temperature drop
per hour?
Course 2, Lesson 5-1
1 4
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6 9
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1 1
10 5
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4 3
7 8
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3 1
2
5 2
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13
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2. Answers
1. 2.
3. 4.
5.
Course 2, Lesson 5-1
1
2
11
1
21
1
7
8
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6
25
1
4
2

3. HOW can you use numbers and
symbols to represent mathematical
ideas?
Expressions and Equations
Course 2, Lesson 5-1

4. Preparation for
• 7.EE.1
Apply properties of operations as strategies to add, subtract, factor, and
expand linear expressions with rational coefficients.
• 7.EE.2
Understand that rewriting an expression in different forms in a problem
context can shed light on the problem and how the quantities in it are
related.
Course 2, Lesson 5-1 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and
Council of Chief State School Officers. All rights reserved.
Expressions and Equations

5. Mathematical Practices
1 Make sense of problems and persevere in solving them.
2 Reason abstractly and quantitatively.
3 Construct viable arguments and critique the reasoning of others.
4 Model with mathematics.
Course 2, Lesson 5-1 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and
Council of Chief State School Officers. All rights reserved.
Expressions and Equations

6. • To evaluate algebraic expressions
• To define variables
• To write algebraic expressions
Course 2, Lesson 5-1
Expressions and Equations

7. Course 2, Lesson 5-1
Expressions and Equations
• variable
• algebraic expression
• algebra
• coefficient
• define a variable

8. 1
Need Another Example?
2
3
Step-by-Step Example
1. Evaluate 2(n + 3) if n = –4.
2(n + 3) = 2(–4 + 3) Replace n with –4.
Evaluate inside the parentheses.
Multiply.
= 2(–1)
= –2

9. Answer
Need Another Example?
Evaluate 3(t – 4) if t = 6.
6

10. 1
Need Another Example?
2
3
Step-by-Step Example
2. Evaluate 8w – 2v if w = 5 and v = 3.
8w – 2v = 8(5) – 2(3) Replace w with 5 and v with 3.
Do all of the multiplication first.
Subtract 6 from 40.
= 40 – 6
= 34

11. Answer
Need Another Example?
Evaluate 6s – 3t if s = 4 and t = –2.
30

12. 1
Need Another Example?
2
3
Step-by-Step Example
3. Evaluate 4y3 + 2 if y = 3.
4y3 + 2 = 4(3)3 + 2 Replace y with 3.
Evaluate the power.
Multiply, then add.
= 4(27) + 2
= 110

13. Answer
Need Another Example?
Evaluate 3m2 – 4 if m = –3.
23

14. 1
Need Another Example?
2
3
4
5
Step-by-Step Example
4. Athletic trainers use the formula , where a
is a person’s age, to find their minimum training heart rate.
Find Latrina’s minimum training heart rate if she is 15 years old.
Replace a with 15.
Subtract 15 from 220.
Multiply 3 and 205.
= 123 Divide 615 by 5.
Latrina’s minimum training heart rate is 123 beats per minute.

15. Answer
Need Another Example?
The formula for rewriting a Fahrenheit temperature
as a Celsius temperature is , where F
equals the temperature in degrees Fahrenheit.
Find the Celsius equivalent of 77° Fahrenheit.
25°C

16. 1
Need Another Example?
2
3
4
Step-by-Step Example
5. Marisa wants to buy a DVD player that costs $150.
She already saved $25 and plans to save an
additional $10 each week. Write an expression
that represents the total amount of money Marisa
has saved after any number of weeks.
savings of $25 plus ten dollars each week
25 + 10w represents the total saved after any number of weeks.
Words
Variable Let w represent the number of weeks.
Expression 25 + 10 • w

17. Answer
Need Another Example?
Leah has already read 20 pages of a book. She
plans to read 5 pages each day from now on.
Write an expression that represents the total
number of pages she will have read in d days.
20 + 5d

18. 1
Need Another Example?
2
3
4
Step-by-Step Example
6. Refer to Example 5. Will Marisa have saved enough
money to buy the $150 DVD player in 11 weeks?
Use the expression 25 + 10w.
25 + 10w = 25 + 10(11) Replace w with 11.
Multiply.
Add.
= 25 + 110
= 135
Marisa will have saved $135 after 11 weeks. Since $135 < $150,
Marisa will not have enough money to buy the DVD player.

19. Answer
Need Another Example?
The expression 20 + 5d represents the total
number of pages Leah will read in d days. Will
Leah have read more than 60 pages in 7 days?
No, she will have only read 55 pages.

20. How did what you learned
today help you answer the
HOW can you use numbers and symbols
to represent mathematical ideas?
Course 2, Lesson 5-1
Expressions and Equations

21. How did what you learned
today help you answer the
HOW can you use numbers and symbols
to represent mathematical ideas?
Course 2, Lesson 5-1
Expressions and Equations
Sample answers:
• To represent unknown values with variables
• To represent real-world situations with algebraic
expressions

22. Describe a real-world
problem with a variable
or variables. Be sure to
define your variable(s).
Course 2, Lesson 5-1
Ratios and Proportional RelationshipsExpressions and Equations