What is the first step needed to solve this equation and what would the equation look like after that first step?

Question

2(2y−10)=20
2
(
2
𝑦
−
10
)
=
20


(1 point)
Responses

Add 10: 2(2y)=30
2
(
2
𝑦
)
=
30
Add 10: 2 times 2 y is equal to 30

Distribute the 2: 4y−40=20
4
𝑦
−
40
=
20
Distribute the 2: 4 y minus 40 is equal to 20

Distribute the 2: 4y−20=20
4
𝑦
−
20
=
20
Distribute the 2: 4 y minus 20 is equal to 20

Distribute the 2: 2y−40=20
2
𝑦
−
40
=
20
Distribute the 2: 2 y minus 40 is equal to 20
Question 2
What is the first step to solve this equation and what would the equation look like after that first step?

2(3y−9)=18
2
(
3
𝑦
−
9
)
=
18

(1 point)
Responses

Add 9 : ​​​​2(3y)=27
2
(
3
𝑦
)
=
27
Add 9 : ​​​​ 2 times 3 y is equal to 27

Distribute the 2: ​​​​​6y−18=36
​
6
𝑦
−
18
=
36
Distribute the 2: ​​​​

Distribute the 2: ​​​​​6y−18=18
​
6
𝑦
−
18
=
18


Distribute the 2: ​​​​

Distribute the 2: ​​​​​2y−18=18
​
2
𝑦
−
18
=
18
Distribute the 2: ​​​​
Question 3
After you combine like terms in this equation, what does it look like?

5=5x−23+2x
5
=
5
𝑥
−
23
+
2
𝑥

(1 point)
Responses

5=3x−23
5
=
3
𝑥
−
23
5 is equal to 3 x minus 23

5=−16x
5
=
−
16
𝑥
5 is equal to negative 16 x

5=7x+23
5
=
7
𝑥
+
23
5 is equal to 7 x plus 23

5=7x−23
5
=
7
𝑥
−
23
5 is equal to 7 x minus 23
Question 4
After you distribute and combine like terms, what does this equation look like?

2(3x+7)+x=70
2
(
3
𝑥
+
7
)
+
𝑥
=
70

(1 point)
Responses

7x+14=70
7
𝑥
+
14
=
70
7 x plus 14 is equal to 70

7x+7=70
7
𝑥
+
7
=
70
7 x plus 7 is equal to 70

6x+7=70
6
𝑥
+
7
=
70
6 x plus 7 is equal to 70

6x+14=70
6
𝑥
+
14
=
70
6 x plus 14 is equal to 70
Question 5
Which of these steps would correctly solve this equation?

5x=−7x+6
5
𝑥
=
−
7
𝑥
+
6

(1 point)
Responses

Add 5x to both sides, then divide by 12, x=12
𝑥
=
1
2
Add 5x to both sides, then divide by 12, x is equal to 1 half

Add 7x to both sides, then divide by 12, x=12
𝑥
=
1
2
Add 7x to both sides, then divide by 12, x is equal to 1 half

Subtract 7x from both sides, then divide by 12, x=12
𝑥
=
1
2
Subtract 7x from both sides, then divide by 12, x is equal to 1 half

Add 7x to both sides, then multiply by 12, x=12

Answer 1

Let's go through the questions one by one.

Question 1

Equation: \( 2(2y−10)=20 \)

First Step: Distribute the 2.

Resulting Equation: \( 4y - 20 = 20 \)

So the best response would be:

• Distribute the 2: \( 4y−20=20 \)

Question 2

Equation: \( 2(3y−9)=18 \)

First Step: Distribute the 2.

Resulting Equation: \( 6y - 18 = 18 \)

So the best response would be:

• Distribute the 2: \( 6y−18=18 \)

Question 3

Equation: \( 5 = 5x - 23 + 2x \)

First Step: Combine like terms on the right side.

Resulting Equation: \( 5 = 7x - 23 \)

So the best response would be:

• 5=7x−23

Question 4

Equation: \( 2(3x+7)+x=70 \)

First Step: Distribute the 2 and then combine like terms.

Resulting Equation:

1. After distribution: \( 6x + 14 + x = 70 \)
2. Combine like terms: \( 7x + 14 = 70 \)

So the best response would be:

• 7x+14=70

Question 5

Equation: \( 5x = -7x + 6 \)

Correct Steps:

1. Add \( 7x \) to both sides: \( 5x + 7x = 6 \) leading to \( 12x = 6 \).
2. Then, divide by 12: \( x = \frac{6}{12} = \frac{1}{2} \).

So the best response would be:

• Add 7x to both sides, then divide by 12, \( x=\frac{1}{2} \)

Feel free to ask if you need further clarification on any of the steps!