## 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 â‰¥ 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
â†’ Can you think of a number that will make this equation true?
Yes. Substituting 10 for r will make a true number sentence.

â†’ 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.

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

â†’ 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
â†’ 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.

â†’ 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.

â†’ 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.

â†’ 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.

â†’ 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.

â†’ Letâ€™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.

â†’ Letâ€™s begin at 6. If I were to subtract 1 from 6, where would that place be on the number line?
5

â†’ 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

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

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

â†’ Letâ€™s try one more. We have already determined that any number greater than or equal to 6 will result in a false number sentence. Letâ€™s try a number greater than 6. Letâ€™s try the number 7.

â†’ 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

â†’ And how many times will we move to the left?
7

â†’ 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.

â†’ 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 â‰  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 â‰¥ 30).

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

f. a – 8 â‰¤ 15
The inequality is true for any value of a that is less than or equal to 23 (a â‰¤ 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 â‰¤ 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 â‰  35).

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

Exercise 4.
$$\frac{h}{5}$$ â‰¥ 12
The inequality is true for any value of h that is greater than or equal to 60 (h â‰¥ 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 â‰¥ 16).

Exercise 6.
4a â‰¤ 16
The inequality is true for any value of a that is less than or equal to 4 (a â‰¤ 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 â‰  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 â‰¥ or â‰¤

Exercise 9.
8.7 ___ 50
> or â‰¥

Exercise 10.
$$\frac{15}{2}$$ ___ 10
< or â‰¤

Exercise 11.
34 ___ 17 . 2
= or â‰¥ or â‰¤

Exercise 12.
18 ___ 24.5 – 6
< or â‰¤

### 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 â‰  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 â‰¥ 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 â‰  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 â‰¤ 32.

Question 5.
d – 8 â‰¥ 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 â‰¥ 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 â‰¥ 2.

Question 7.
10 – h â‰¤ 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 â‰¥ 3 and false when h < 3.

Question 8.
42 + 8 â‰¥ 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 â‰  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 â‰¤ 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 â‰  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 â‰¤ a + 8