Question 1

Question

Question 1
Shawn is solving this equation:

𝑥
7
−
47
=
−
6
7
x
​
 −47=−6
One of his steps is to multiply both sides of the equation by 7. Why?

Multiplying both sides by 7 undoes the addition in the original problem.
Multiplying both sides by 7 undoes the subtraction in the original problem.
Multiplying both sides by 7 undoes the division of 
𝑥
x by 7 in the original problem.
The negative sign in -6 must be changed to positive.
Question 2
Which of the following is equivalent to this equation?

63
−
3
(
2
−
10
𝑤
)
=
150
63−3(2−10w)=150
120
−
10
𝑤
=
150
120−10w=150
120
−
600
𝑤
=
150
120−600w=150
−
10
𝑤
=
150
−10w=150
57
+
30
𝑤
=
150
57+30w=150
Question 3
A) Correctly select the order of the steps to solve this equation:

−
5
𝑥
+
2
=
67
−5x+2=67
Add 67 to both sides.
Add 2 to both sides.
Add 5 to both sides.
Divide both sides by -5.
Multiply by -5 on both sides.
Subtract 2 from both sides.
B) Solve for 
𝑥
x:

𝑥
=
−
3
x=−3
𝑥
=
5
x=5
𝑥
=
−
69
5
x=− 
5
69
​
 
𝑥
=
13
x=13
Question 4
A) Correctly select the order of the steps to solve this equation:

𝑟
5
−
6
=
−
1
5
r
​
 −6=−1
Add 5 to both sides.
Multiply by 5 on both sides.
Add 6 to both sides.
Subtract 6 from both sides.
Divide both sides by 5.
B) Solve for 
𝑟
r:

𝑟
=
5
r=5
𝑟
=
25
r=25
𝑟
=
35
r=35
𝑟
=
10
r=10
Question 5
A) Correctly select the order of the steps to solve this equation:

−
8
−
3
𝑥
=
10
−8−3x=10
Add 8 to both sides.
Add 3 to both sides.
Add 10 to both sides.
Multiply both sides by 3.
Divide both sides by 3.
Divide both sides by -3.
Subtract 8 from both sides.
Subtract 3 from both sides.
B) Solve for 
𝑥
x:

𝑥
=
−
54
x=−54
𝑥
=
−
6
x=−6
𝑥
=
54
x=54
𝑥
=
6
x=6
Question 6
Select the TWO expressions that are equivalent to the given expression:

(
2
𝑥
+
2
)
−
(
3
𝑥
+
11
)
(2x+2)−(3x+11)
−
𝑥
−
9
−x−9
2
𝑥
−
3
𝑥
+
2
+
11
2x−3x+2+11
−
𝑥
+
13
−x+13
5
𝑥
+
13
5x+13
2
𝑥
−
3
𝑥
+
2
−
11
2x−3x+2−11
5
𝑥
+
9
5x+9
−
𝑥
+
9
−x+9
Question 7
Simplify the expression:

6
(
3
𝑥
−
5
)
+
2
(
3
𝑥
−
5
)
−
8
(
2
𝑥
−
5
)
6(3x−5)+2(3x−5)−8(2x−5)
8
𝑥
8x
24
𝑥
−
40
24x−40
36
𝑥
−
60
36x−60
48
𝑥
−
80
48x−80
Question 8
Celeste planted six trees, each 8 feet tall. She expects them to grow over 5 years. Assume 
𝑥
x represents the number of years from when the trees were planted. Which of the following equations represents the height of each tree in 5 years?

Sycamore: 
8
+
2.5
𝑥
=
12.5
8+2.5x=12.5
Sugar Maple: 
8
+
1.5
𝑥
=
15.5
8+1.5x=15.5
Red Maple: 
8
𝑥
+
3
=
43
8x+3=43
Linden: 
8
𝑥
+
1.5
=
9.5
8x+1.5=9.5
Oak: 
8
+
4
𝑥
=
28
8+4x=28
Question 9
A) Correctly select the steps to solve the given equation:

3
𝑥
−
7
−
2
𝑥
+
5
=
6
3x−7−2x+5=6
Step 1: Use the commutative property to combine like terms.
Step 2: Combine the variables and constants.
Step 3: Use one more operation to solve for 
𝑥
x.
B) Solve for 
𝑥
x:

𝑥
=
7
x=7
𝑥
=
−
8
x=−8
𝑥
=
8
x=8
𝑥
=
4
x=4
Question 10
In Atlanta, the temperature was -2°F in the morning. After a winter storm, it dropped 10 degrees. What is the temperature now?

Question 11
A mountain climber starts at 380 ft. above sea level. At his first stop, he climbed 182 ft. and at his second stop another 208 ft. He then descended 235 ft. How much further does he need to descend to return to his starting point?

155 feet
78 feet
535 feet
235 feet
Question 12
Tickets to a baseball game are on sale for $1.50 off the regular price. Dea buys 6 tickets, and her total cost is $51. Which equation represents this situation?

6
(
𝑟
−
1.50
)
=
51
6(r−1.50)=51
6
(
𝑟
+
1.50
)
=
51
6(r+1.50)=51
6
𝑟
−
1.50
=
51
6r−1.50=51
6
𝑟
+
1.50
=
51
6r+1.50=51
Question 13
Which situation is best represented by this equation?

12
ℎ
+
30
=
258
12h+30=258
Eric was paid $30 last week, with a $258 bonus and $12 per hour. What is 
ℎ
h?
Eric was paid $258 last week, with a $12 bonus and $30 per hour. What is 
ℎ
h?
Eric was paid $258 last week, with a $30 bonus and $12 per hour. What is 
ℎ
h?
Eric was paid $30 last week, with a $12 bonus and $258 per hour. What is 
ℎ
h?
Question 14
A) Correctly select the order of the steps to solve this equation:

1
3
(
6
𝑥
−
9
)
=
−
33
3
1
​
 (6x−9)=−33
Step 1: Add or subtract to isolate terms.
Step 2: Multiply or divide to solve.
B) Solve for 
𝑥
x:

𝑥
=
−
30
x=−30
𝑥
=
−
15
x=−15
𝑥
=
−
22
x=−22
𝑥
=
−
19
x=−19
Question 15
A) List the steps to solve this equation:

−
3
5
(
15
𝑥
−
30
)
=
198
− 
5
3
​
 (15x−30)=198
B) Solve for 
𝑥
x:

𝑥
=
−
24
x=−24
𝑥
=
−
36
x=−36
𝑥
=
−
10
x=−10
𝑥
=
−
20
x=−20
Question 16
At Mariah's birthday, 9 friends ate 
3
4
4
3
​
  of her cake. How much of the cake did each friend eat?

12
3
3
12
​
 
6
4
4
6
​
 
1
9
9
1
​
 
1
12
12
1

GPT-4o mini · Answer

Here are the answers to the questions you provided:

Question 1

Why does Shawn multiply both sides by 7?

Multiplying both sides by 7 undoes the division of $ x $ by 7 in the original problem.

Question 2

Which of the following is equivalent to the equation $ 63 - 3(2 - 10w) = 150 $?

120 - 600w = 150

Question 3

A) Correct order of steps to solve the equation $ -5x + 2 = 67 $:

Add 5 to both sides.
Subtract 2 from both sides.
Divide both sides by -5.

B) Solve for $ x $:

$ x = -13 $

Question 4

A) Correct order of steps to solve the equation $ \frac{r}{5} - 6 = -1 $:

Add 6 to both sides.
Multiply by 5 on both sides.

B) Solve for $ r $:

$ r = 25 $

Question 5

A) Correct order of steps to solve the equation $ -8 - 3x = 10 $:

Add 8 to both sides.
Divide both sides by -3.

B) Solve for $ x $:

$ x = -6 $

Question 6

Select the TWO expressions that are equivalent to $ (2x + 2) - (3x + 11) $:

-x - 9
-x + 13

Question 7

Simplify the expression $ 6(3x - 5) + 2(3x - 5) - 8(2x - 5) $:

36x - 60

Question 8

Which equation represents the height of each tree in 5 years (assuming $ x $ is years from planting):

Oak: $ 8 + 4x = 28 $

Question 9

A) Correct steps to solve the equation $ 3x - 7 - 2x + 5 = 6 $:

Step 1: Use the commutative property to combine like terms.
Step 2: Combine the variables and constants.
Step 3: Use one more operation to solve for $ x $.

B) Solve for $ x $:

$ x = 8 $

Question 10

What is the temperature now?

The temperature now is $(-2 - 10) = -12°F$.

Question 11

How much further does the mountain climber need to descend to return to his starting point?

The climber starts at 380 ft.
- Climbed: 182 ft + 208 ft = 390 ft.
- Descended: 235 ft.
- Total height now = 380 ft + 390 ft - 235 ft = 535 ft.
To return to the starting point: $ 535 - 380 = 155 $ feet.
Answer: 155 feet.

Question 12

Which equation represents the situation?

$ 6(r - 1.50) = 51 $

Question 13

Which situation is best represented by the equation $ 12h + 30 = 258 $?

Eric was paid $30 last week, with a $12 bonus and $258 per hour. What is $ h $?

Question 14

A) Correct order of steps to solve $ \frac{1}{3}(6x - 9) = -33 $:

Step 1: Add or subtract to isolate terms.
Step 2: Multiply or divide to solve.

B) Solve for $ x $:

$ x = -22 $

Question 15

A) List the steps to solve the equation $ -\frac{3}{5}(15x - 30) = 198 $:

Distribute $-\frac{3}{5}$ across $ (15x - 30) $.
Multiply or divide to isolate $ x $.

B) Solve for $ x $:

$ x = -24 $

Question 16

At Mariah's birthday, how much did each friend eat?

Total cake eaten: $ \frac{3}{4} $ divided by 9 friends = $ \frac{3/4}{9} = \frac{3}{36} = \frac{1}{12} $.
Each friend ate $ \frac{1}{12} $ of the cake.

Feel free to ask if you need more information or clarification on any of these questions!