## Engage NY Eureka Math Grade 6 Module 4 Lesson 24 Answer Key

### Eureka Math Grade 6 Module 4 Lesson 24 Opening Exercise Answer Key

Opening Exercise:

State whether each number sentence is true or false. If the number sentence is false, explain why.

a. 4 + 5 > 9
False. 4 + 5 is not greater than 9.

b. 36 = 18
True

c. 32 > $$\frac{64}{4}$$
True

d. 78 – 15 < 68
True

e. 22 ≥ 11 + 12
False. 22 is not greater than or equal to 23.

### Eureka Math Grade 6 Module 4 Lesson 24 Example Answer Key

Example 1:

Write true or false if the number substituted for g results in a true or false number sentence.  Example 2:

State when the following equations/inequalities will be true and when they will be false.

a. r + 15 = 25
→ Can you think of a number that will make this equation true?
Yes. Substituting 10 for r will make a true number sentence.

→ Is 10 the only number that results in a true number sentence? Why or why not?
Yes. There is only one value that, if substituted, will result in a true number sentence. There is only one number that can be added to 15 to get exactly 25.

→ What will make the number sentence false?
Any number that is not 10 will result in a false number sentence.

→ If we look back to the original questions, how can we state when the equation will be true? False?
The equation is true when the value substituted for r is 10 and false when the value of r is any other number.

b. 6 – d > 0
→ If we wanted 6 – d to equal 0, what would the value of d have to be? Why?
The value of d would have to be 6 because 6 – 6 = 0.

→ Will substituting 6 for d result in a true number sentence? Why or why not?
If d has a value of 6, then the resulting number sentence would not be true because the left side has to be greater than 0, not equal to 0.

→ How about substituting 5 for d? 4? 3? 2?
Yes. Substituting any of these numbers for d into the inequality results in true number sentences.

→ What values can we substitute for d in order for the resulting number sentence to be true?
The inequality is true for any value of d that is less than 6.

→ What values for d would make the resulting number sentence false?
The inequality is false for any value of d that is greater than or equal to 6.

→ Let’s take a look at a number line and see why these statements make sense.

Display a number line on the board. Label the number line as shown below. → Let’s begin at 6. If I were to subtract 1 from 6, where would that place be on the number line?
5

→ So, if we substitute 1 for d, then 6 – 1 = 5, and the resulting number sentence is true. How about if I subtracted 2 from 6? Would our number sentence be true for the value 2?
Yes

→ What if I subtracted 6 from the 6 on the number line? Where would that be on the number line?
0

→ So, if we substitute 6 for d, will the resulting number sentence be true or false?
False

→ Let’s try one more. We have already determined that any number greater than or equal to 6 will result in a false number sentence. Let’s try a number greater than 6. Let’s try the number 7.

→ Start with the 6 on the number line. If we were to subtract 7, in which direction on the number line would we
move?
To the left

→ And how many times will we move to the left?
7

→ Model beginning at 6 on the number line, and move a finger, or draw the unit skips, while continually moving to the left on the number line 7 times. → So, it seems we have ended up at a place to the left of O. What number is represented by this position?
-1

c. $$\frac{1}{2}$$f = 15
The equation is true when the value substituted for fis 30 (f = 30) and false when the value off is any other number (f ≠ 30).

d. $$\frac{y}{3}$$ < 10
The inequality is true for any value of y that is less than 30 (y < 30) and false when the value of y is greater than or equal to 30 (y ≥ 30).

e. 7g ≥ 42
The inequality is true for any value of g that is greater than or equal to 6 (g ≥ 6) and false when the value of g is less than (g < 6).

f. a – 8 ≤ 15
The inequality is true for any value of a that is less than or equal to 23 (a ≤ 23) and false when the value of a is greater than 23 (a > 23).

### Eureka Math Grade 6 Module 4 Lesson 24 Exercise Answer Key

Exercises:

Complete the following problems in pairs. State when the following equations and inequalities will be true and when they will be fake.

Exercise 1.
15c > 45
The inequality is true for any value of c that is greater than 3 (c > 3) and false when the value of c is less than or equal to (c ≤ 3).

Exercise 2.
25 = d – 10
The equation is true when the value of d is 35 (d = 35) and false when the value of d is any other number (d ≠ 35).

Exercise 3.
56 ≥ 2e
The inequality is true for any value of e that is less than or equal to 28 (e ≤ 28) and false when the value of e is greater than 8 (e > 28).

Exercise 4.
$$\frac{h}{5}$$ ≥ 12
The inequality is true for any value of h that is greater than or equal to 60 (h ≥ 60) and false when the value of h is less than (h < 60).

Exercise 5.
45 > h + 29
The inequality is true for any value of h that is less than 16 (h < 16) and false when the value of h is greater than or
equal to 16 (h ≥ 16).

Exercise 6.
4a ≤ 16
The inequality is true for any value of a that is less than or equal to 4 (a ≤ 4) and false when the value of a is greater than (a > 4).

Exercise 7.
3x = 24
The equation is true when the value of x is 8 (x = 8) and false when the value of x is any other number (x ≠ 8).

Identify all equality and inequality signs that can be placed into the blank to make a true number sentence.

Exercise 8.
15 + 9 ___ 24
= or ≥ or ≤

Exercise 9.
8.7 ___ 50
> or ≥

Exercise 10.
$$\frac{15}{2}$$ ___ 10
< or ≤

Exercise 11.
34 ___ 17 . 2
= or ≥ or ≤

Exercise 12.
18 ___ 24.5 – 6
< or ≤

### Eureka Math Grade 6 Module 4 Lesson 24 Problem Set Answer Key

State when the following equations and inequalities will be true and when they will be false.

Question 1.
36 = 9k
The equation is true when the value of k is 4 and false when the value of k is any number other than 4.
OR
The equation is true when k = 4 and false when k ≠ 4.

Question 2.
67 > f – 15
The inequality is true for any value off that is less than 82 and false when the value of f is greater than or equal to 82.
OR
The inequality is true when f < 82 and false when f ≥ 82.

Question 3.
$$\frac{v}{9}$$ = 3
The equation is true when the value of v is 27 and false when the value of v is any number other than 27.
OR
The equation is true when v = 27 and false when v ≠ 27.

Question 4.
10 + b > 42
The inequality is true for any value of b that is greater than 32 and false when the value of b is less than or equal to 32.
OR
The inequality is true when b > 32 and false when b ≤ 32.

Question 5.
d – 8 ≥ 35
The inequality is true for any value of d that is greater than or equal to 43 and false when the value of d is less than 43
OR
The inequality is true when d ≥ 43 and false when d <43.

Question 6.
32f < 64
The inequality is true for any value of f that is less than 2 and false when the value off is greater than or equal to 2.
OR
The inequality is true when f < 2 and false when f ≥ 2.

Question 7.
10 – h ≤ 7
The inequality is true for any value of h that is greater than or equal to 3 and false when the value of h is less than 3.
OR
The inequality is true when h ≥ 3 and false when h < 3.

Question 8.
42 + 8 ≥ g
The inequality is true for any value of g that is less than or equal to 50 and false when the value of g is greater than 50.
OR
The inequality is true when g < 50 and false when g > 50.

Question 9.
$$\frac{m}{3}$$ = 14
The equation is true when the value of m is 42 and false when the value of m is any number other than 42.
OR
The equation is true when m = 42 and false when m ≠ 42.

### Eureka Math Grade 6 Module 4 Lesson 24 Exit Ticket Answer Key

State when the following equations and inequalities will be true and when they will be false.

Question 1.
5g > 45
The inequality is true for any value of g that is greater than 9 and false when the value of g is less than or equal to 9.
OR
The inequality is true when g > 9 and false when g ≤ 9.

Question 2.
14 = 5 + k
The equation is true when the value of k is 9 and false when the value of k is any other number.
OR
The equation is true when k = 9 and false when k ≠ 9.

Question 3.
26 – w < 12
The inequality is true for any value of w that is greater than 14 and false when the value of w is less than or equal to 14.
OR
The inequality is true when w > 14 and false when w < 14.

Question 4.
32 ≤ a + 8