## Engage NY Eureka Math Grade 6 Module 4 Lesson 33 Answer Key

### Eureka Math Grade 6 Module 4 Lesson 33 Example Answer Key

Example 1:

What value(s) does the variable have to represent for the equation or inequality to result in a true number sentence? What value(s) does the variable have to represent for the equation or inequality to result in a false number sentence?

a. y + 6 = 16

Answer:

The number sentence is true when y is 10. The sentence is false when y is any number other than 10.

b. y + 6 > 16

Answer:

The number sentence is true when y is any number greater than 10. The sentence is false when y is 10 or any number less than 10.

c. y + 6 ≥ 16

Answer:

The number sentence is true when y is 10 or any number greater than 10. The sentence is fake when y is a number less than 10.

d. 3g = 15

Answer:

The number sentence is true when g is 5. The number sentence is false when g is any number other than 5.

e. 3g < 15

Answer:

The number sentence is true when g is any number less than 5. The number sentence is false when g is 5 or any number greater than 5.

f. 3g ≤ 15

Answer:

The number sentence is true when g is 5 or any number less than 5. The number sentence is false when g is any number greater than 5.

Example 2:

Which of the following number(s), if any, make the equation or inequality true: (0, 3, 5, 8, 10, 14)?

a. m + 4 = 12

Answer:

m = 8 or (8)

b. m + 4 < 12

Answer:

(0, 3, 5)

→ How does the answer to part (a) compare to the answer to part (b)?

In part (a), 8 is the only number that will result in a true number sentence. But in part (b), any number in the set that is less than 8 will make the number sentence true.

c. f – 4 = 2

Answer:

None of the numbers in the set will result in a true number sentence.

d. f – 4 > 2

Answer:

(8, 10, 14)

→ Is there a number that we could include in the set so that part (c) will have a solution?

Yes. The number 6 will make the equation in part (c) true.

→ Would 6 be part of the solution set in part (d)?

No. The 6 would not make port (d) a true number sentence because 6 – 4 is not greater than 2.

→ How could we change part (d) so that 6 would be part of the solution?

Answers will vary; If the > was changed to a ≥, we could include 6 in the solution set.

e. \(\frac{1}{2}\)h = 8

Answer:

None of the numbers in the set will result in a true number sentence.

f. \(\frac{1}{2}\)h ≥ 8

Answer:

None of the numbers in the set will result in a true number sentence.

→ Which whole numbers, if any, make the inequality in part (f) true?

Answers will vary; 16 and any number greater than 16 will make the number sentence true.

### Eureka Math Grade 6 Module 4 Lesson 33 Exercise Answer Key

Exercises:

Choose the number(s), if any, that make the equation or inequality true from the following set of numbers: (0, 1, 5, 8, 11, 17).

Exercise 1.

m + 5 = 6

Answer:

m= 1 or {1)

Exercise 2.

m + 5 ≤ 6

Answer:

(0, 1)

Exercise 3.

5h = 40

Answer:

h = 8 or (8)

Exercise 4.

5h > 40

Answer:

(11, 17)

Exercise 5.

\(\frac{1}{2}\)y = 5

Answer:

There is no solution in the set.

Exercise 6.

\(\frac{1}{2}\)y ≤ 5

Answer:

(0, 1, 5, 8)

Exercise 7.

k – 3 = 20

Answer:

There is no solution in the set.

Exercise 8.

k – 3 > 20

Answer:

There is no solution in the set.

### Eureka Math Grade 6 Module 4 Lesson 33 Problem Set Answer Key

Choose the number(s), if any, that make the equation or inequality true from the following set of numbers: (0, 3, 4, 5, 9, 13, 18, 24).

Question 1.

h – 8 = 5

Answer:

h = 13 or (13)

Question 2.

h – 8 < 5

Answer:

(0, 3, 4, 5, 9)

Question 3.

4g = 36

Answer:

g = 9 or (9)

Question 4.

4g ≥ 36

Answer:

(9, 13, 18, 24)

Question 5.

\(\frac{1}{4}\)y = 7

Answer:

There is no number in the set that will make this equation true.

Question 6.

\(\frac{1}{4}\)y > 7

Answer:

There is no number in the set that will make this inequality true.

Question 7.

m – 3 = 10

Answer:

m = 13 or (13)

Question 8.

m – 3 ≤ 10

Answer:

{0, 3, 4, 5, 9, 13}

### Eureka Math Grade 6 Module 4 Lesson 33 Exit Ticket Answer Key

Choose the number(s), if any, that make the equation or inequality true from the following set of numbers: {3,4, 7, 9, 12, 18, 32).

Question 1.

\(\frac{1}{3}\)f = 4

Answer:

f = 12 or {12}

Question 2.

\(\frac{1}{3}\)f < 4

Answer:

{3, 4, 7, 9)

Question 3.

m + 7 = 20

Answer:

There is no number in the set that will make this equation true.

Question 4.

m + 7 ≥ 20

Answer:

{18, 32}