1. Module 4 Lesson 33 From Equations to Inequalities.notebook
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Problem Set Lesson 32 Answers

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MODULE 4 Expressions and Equaons
Topic G: Solving Equaons
Lesson 33: From Equaons to Inequalies
Student Outcomes
§ Students understand that an inequality with numerical expressions is either
true or false. It is true if the numbers calculated on each side of the inequality
sign result in a correct statement and false otherwise.
§ Students understand solving an inequality is answering the queson of which
values from a specified set, if any, make the inequality true.

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Classwork Example 1
What value(s) does the variable have to represent for the number sentence to be a
true statement? What value(s) does the variable have to represent for the number
sentence to be a false statement?
a. y + 6 = 16 b. y + 6 > 16 c. y + 6 ≥ 16
What do you notice that is the same & different between "a", "b", & "c"?
true: false: true: false: true: false:

7. Module 4 Lesson 33 From Equations to Inequalities.notebook
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d. 3g = 15 e. 3g < 15 f. 3g ≤ 15
What do you notice that is the same & different between "d", "e", & "f"?
true: false: true: false: true: false:

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Example 2
Which of the following numbers from this set make the equaon true?
{0, 3, 5, 8, 10, 14}0 3 5 8 10 14
a. m + 4 = 12 b. m + 4 < 12
How does the answer in part "a" compare to the answer in part "b"?
8 530

9. Module 4 Lesson 33 From Equations to Inequalities.notebook
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Which of the following numbers from this set make the equaon true?
{0, 3, 5, 8, 10, 14}0 3 5 8 10 14
c. f ­ 4 = 2 d. f ­ 4 > 2
Is there a number that we could include in the set so that part "c" will
have a solution?
Would it be a part of the solution set for part "d"?
HOw could we change "d" so that it would be part of the solution?
8 10 14

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Which of the following numbers from this set make the equaon true?
{0, 3, 5, 8, 10, 14}0 3 5 8 10 14
e. ½h = 8 f. ½h ≥ 8
Which whole numbers, if any, make the equation true?
Which whole numbers, if any, make the inequality true?

11. Module 4 Lesson 33 From Equations to Inequalities.notebook
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Exercises
Choose the numbers that make the equaon or
inequality true from the following set of numbers:
{0, 1, 5, 8, 11, 17}
1. m + 5 = 6 2. m + 5 ≤ 6
3. 5h = 40 4. 5h > 40
0 1 5 8 11 17
1 0 1
8 11 17

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Exercises
Choose the numbers that make the equaon or inequality true from the
following set of numbers:
{0, 1, 5, 8, 11, 17}
5. ½y = 5 6. ½y ≤ 5
7. k ­ 3 = 20 8. k ­ 3 > 20
0 1 5 8 11 17
8
8
510

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Closing
Please take out your exit ticket for Lesson 33, close your
binder, and complete the exit ticket. This will be collected.
§ In some of the equaons and inequalies we worked within this lesson none
of the numbers in the given set were soluons. What does this mean? Are
there numbers that will make the statements true that are not in the set?
None of the numbers in the set made a true statement. There are numbers
that could make the statement true. For example, in Exercise 5 ½y = 5, y = 10
would make it a true statement.
§ Is it possible for every number in a set to make a true statement?
Yes it is possible. For example, if the inequality says x > 5 and all the numbers in
the set are greater than 5, then all the numbers in the set will make a true
statement.