(8) Lesson 2.3 - Write Two-Step Equations

1. Course 3, Lesson 2-3
Solve each equation. Check your solution.
1. 3n + 2 = 8
2. 6n − 3 = 21
3. 2 = 3 − a
4. −5 + 2a − 3a = 11
5. Jack traveled 5 miles plus 3 times as many miles as Janice.
He traveled 23 miles in all. How far did Janice travel?
6. If 3x − 2 = 16, what is the value of 2x − 3?

2. Course 3, Lesson 2-3
Answers
1. 2
2. 4
3. 1
4. −16
5. 6 miles
6. 9

3. WHAT is equivalence?
Expressions and Equations
Course 3, Lesson 2-3

4. • 8.EE.7
Solve linear equations in one variable.
• 8.EE.7a
Give examples of linear equations in one variable with one solution,
infinitely many solutions, or no solutions. Show which of these possibilities
is the case by successively transforming the given equation into simpler
forms, until an equivalent equation of the form x = a, a = a, or a = b results
(where a and b are different numbers).
• 8.EE.7b
Solve linear equations with rational number coefficients, including
equations whose solutions require expanding expressions using the
distributive property and collecting like terms.
Course 3, Lesson 2-3 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 3, Lesson 2-3 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
• translate sentences into equations
• define a variable, then write and
solve equations
Course 3, Lesson 2-3
Expressions and Equations

7. 1
Need Another Example?
2
Step-by-Step Example
1. Translate the sentence into an equation.
Eight less than three times a number is –23.
Eight less than three times a number is –23.Words
3
Let n represent the number.Variable
3n – 8 = –23Equation

8. Answer
Need Another Example?
Translate three more than half a number is 15
into an equation.
n + 3 = 15

9. 1
Need Another Example?
2
3
Step-by-Step Example
2. Translate the sentence into an equation.
Thirteen is 7 more than one-fifth of a number.
Thirteen is 7 more than one-fifth of a number.Words
Let n represent the number.Variable
Equation 13 = n + 7

10. Answer
Need Another Example?
Translate nineteen is two more than five times
a number into an equation.
19 = 5n + 2

11. 1
Need Another Example?
2
3
4
5
6
Step-by-Step Example
3. You buy 3 books that each cost the same amount and
a magazine, all for $55.99. You know that the magazine
costs $1.99. How much does each book cost?
3b + 1.99 = 55.99
So, the books each cost $18.7
Three books and a magazine cost $55.99.Words
Let b represent the cost of one book.Variable
3b + 1.99 = 55.99Equation
Write the equation.
Subtraction Property of Equality
Simplify.3b = 54.00
Division Property of Equality
b = 18 Simplify.
–1.99 = – 1.99

12. Answer
Need Another Example?
Kendra paid $7 for her admission ticket to the fair and
bought 12 ride tickets. She spent a total of $31 on
admission and ride tickets. Write and solve an equation to
find the cost of one ride ticket.
7 + 12x = 31; $2

13. 1
Need Another Example?
2
3
4
5
6
Step-by-Step Example
4. A personal trainer buys a weight bench for $500 and w
weights for $24.99 each. The total cost of the purchase
is $849.86. How many weights were purchased?
500 + 24.99w = 849.86
Bench plus $24.99 per weight equals $849.86Words
Let w represent the number of weights.Variable
500 + 24.99 • w = 849.86Equation
Write the equation.
Subtraction Property of Equality
Simplify.24.99w = 349.86
Division Property of Equality
w = 14 Simplify.
So, 14 weights were purchased.
–500 = – 500

14. Answer
Need Another Example?
Membership at the health club is $15 per month
plus $10 for each exercise class taken. Jill paid
$75 for the month of September. Write and solve
an equation to find the number of exercise
classes Jill took in September.
15 + 10c = 75; 6 classes

15. 1
Need Another Example?
2
3
4
5
6
Step-by-Step Example
5. Your and your friend’s lunch cost $19. Your lunch
cost $3 more than your friend’s. How much was
your friend’s lunch?
f + f + 3 = 19
Your friend’s lunch plus your lunch equals $19.Words
Let f represent the cost of your friend’s lunch.Variable
f + f + 3 = 19Equation
Write the equation.
Subtraction Property of Equality
Simplify.2f = 16
Division Property of Equality
f = 8 Simplify.
Your friend spent $8.
2f + 3 = 19 f + f = 2f
–3 = – 3

16. Answer
Need Another Example?
You and your friend spent a total of $33 for dinner. Your
dinner cost $5 less than your friend’s. Write and solve an
equation to find how much you spent for dinner.
d + (d – 5) = 33; $14

17. How did what you learned
today help you answer the
WHAT is equivalence?
Course 3, Lesson 2-3
Expressions and Equations

18. How did what you learned
today help you answer the
WHAT is equivalence?
Course 3, Lesson 2-3
Expressions and Equations
Sample answers:
• You can use a two-step equation to represent a real-
world situation.
• Words can translate into variables and equations.

19. Write an equation for the
following situation:
An appliance repairman
charges $35 for a house
call and $30 per hour. The
cost of a house call and
repair job came to $125.
Ratios and Proportional RelationshipsExpressions and Equations
Course 3, Lesson 2-3