(7) Lesson 6.2

1. Solve each equation. Check your solution.
1. x + 31 = 53
2. –5 + y = 13
3. r – 7. 2 = 22.8
4. –11 = 8 + a
5. Write and solve an equation to
determine Dale’s top speed at
the racetrack if Dale’s top speed
was 17 mph less than Andy’s.
Course 2 Lesson 6-2

2. Course 2 Lesson 6-2
ANSWERS
1. x = 22
2. y = 18
3. r = 30
4. a = –19
5. 17 + s = 152; s = 135 mph

3. WHAT does it mean to say
two quantities are equal?
Expressions and Equations
Course 2 Lesson 6-2

4. • 7.EE.4
Use variables to represent quantities in a real-world or mathematical
problem, and construct simple equations and inequalities to solve
problems by reasoning about the quantities.
• 7.EE.4a
Solve real-world problems leading to equations of the form px + q = r
and p(x + q) = r, where p, q, and r are specific rational numbers. Solve
equations of these forms fluently. Compare an algebraic solution to an
arithmetic solution, identifying the sequence of operations used in each
approach.
Course 2 Lesson 6-2 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.
7 Look for and make use of structure.
Course 2 Lesson 6-2 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. How to solve equations using:
• The Division Property of Equality
• The Multiplication Property of
Equality
Course 2 Lesson 6-2
Expressions and Equations

7. Course 2 Lesson 6-2
Expressions and Equations
• coefficient
• Division Property of Equality
• Multiplication Property of Equality

8. Course 2 Lesson 6-2
Expressions and Equations
Division Property of EqualityWords The states that the two
sides of an equation remain equal when you divide each
side by the same nonzero number.
Symbols If a = b, and c ≠ 0, then .
a b
c c


9. 1
Need Another Example?
2
3
4
5
Step-by-Step Example
1. Solve 20 = 4x. Check your solution.
Write the equation.
Simplify.
Check 20 = 4x Write the original equation.
So, the solution is 5.
5 = x
20 = 4x
Division Property of Equality
20 = 4(5)
20 = 20
Replace x with 5.
This sentence is true.
?

10. Answer
Need Another Example?
Solve 39 = 3y. Check your solution.
13

11. 1
Need Another Example?
2
3
4
5
Step-by-Step Example
2. Solve –8y = 24. Check your solution.
Write the equation.
Simplify.
Check –8y = 24 Write the original equation.
So, the solution is –3.
y = –3
–8y = 24
Division Property of Equality
–8(–3) = 24
24 = 24
Replace y with –3.
This sentence is true.
?

12. Answer
Need Another Example?
Solve −4z = 60. Check your solution.
–15

13. 1
Need Another Example?
2
3
4
5
Step-by-Step Example
3. Lelah sent 574 text messages last week. On average,
how many messages did she send each day?
Division Property of Equality
Simplify.
Lelah sent 82 messages on average each day.
82 = m
574 = 7m Write the equation. There are 7 days in one week.
Let m represent the number of messages Lelah sent.

14. Answer
Need Another Example?
Serena mailed 138 letters during the last 6 days.
Write and solve an equation to find on average,
how many letters she mailed each day.
6x = 138; 23 letters

15. Course 2 Lesson 6-2
Expressions and Equations
Multiplication Property of EqualityWords The states that the
two sides of an equation remain equal if you multiply each
side by the same number.
Symbols If a = b, then ac = bc.

16. 1
Need Another Example?
2
3
Step-by-Step Example
4. Solve = –9.
Simplify.a = 36
= –9 Write the equation.
Multiplication Property of Equality= –9(–4)(–4)

17. Answer
Need Another Example?
Solve = −10. Check your solution.
−20

18. 1
Need Another Example?
2
3
4
Step-by-Step Example
5. The distance d Tina travels in her car while driving
60 miles per hour for 3 hours is given by the equation
= 60. How far did she travel?
Simplify.d = 180
= 60 Write the equation.
Multiplication Property of Equality
Tina traveled 180 miles.
(3) = 60(3)

19. Answer
Need Another Example?
The distance d that Lee travels on his bike at a
rate of 20 miles per hour for 4 hours is given by
the equation = 20. How far did he ride?
80 mi

20. How did what you learned
today help you answer the
WHAT does it mean to say
two quantities are equal?
Course 2 Lesson 6-2
Expressions and Equations

21. How did what you learned
today help you answer the
WHAT does it mean to say
two quantities are equal?
Course 2 Lesson 6-2
Expressions and Equations
Sample answers:
• To solve equations using the Division Property of
Equality
• To solve equations using the Multiplication Property of
Equality

22. Use the formula
d = rt to write and
solve a rate problem.
Ratios and Proportional RelationshipsExpressions and Equations
Course 2 Lesson 6-2