Solve this equation for y: 7y=12x(1 point)

Question

Responses

y=12x−7y is equal to 12 x minus 7

y=12x+7y is equal to 12 x plus 7

y=712xy is equal to 7 over 12 x

y=127xy is equal to 12 sevenths x
Question 2
8. Change the equation from standard form to slope-intercept form by solving for y.

8x−4y=24
Determine who changed the equation correctly:

Bob:

Subtract 8x from both sides: −4y=−8x+24
Divide by -4 on both sides: y=2x−6
Bill:

Subtract 8x from both sides: −4y=16x
Divide by -4 on both sides: y=−4x
Bud:

Subtract 8x from both sides: −4y=−8x+24
Divide by -4 on both sides: y=2x+24


(1 point)
Responses

Bill
Bill

Bob
Bob

Bud
Bud

None of them are correct
None of them are correct
Question 3
9. Solve 3x+2b=6c for x.

Step 1: 3x+2b−2b=6c−2b subtract 2b from both sides

Step 2: 3x=6c−2b combine like terms/simplify

Step 3: 3x3=6c3−2b divide by 3 on both sides to get x isolated

Step 4: x=2c−2b simplify/final answer

Which statement is TRUE?

(1 point)
Responses

The process has an error. The correct answer is x=−4b−cThe process has an error. The correct answer is x is equal to negative 4 b minus c

The process is correct.
The process is correct.

The process has an error. The correct answer is x=2c−23bThe process has an error. The correct answer is x is equal to 2 c minus 2 thirds b

The process has an error. The correct answer is x=4bc3

Answer 1

Let's solve the equations and evaluate the responses one by one:

Question 1

Solve the equation for y:
7y = 12x

To isolate y, divide both sides by 7: \[ y = \frac{12x}{7} \]
This gives us: \[ y = \frac{12}{7}x \] or equivalently \( y = \frac{12}{7}x \)

Correct Response: \[ y = \frac{12}{7}x \text{ is equal to } \frac{12}{7}x \]

Question 2

Change the equation from standard form to slope-intercept form:
\[ 8x - 4y = 24 \]

Bob's Steps:

1. Subtract \( 8x \): \(-4y = -8x + 24\)
2. Divide by \(-4\): \( y = 2x - 6 \) (This step is correct.)

Bill's Steps:

1. Subtract \( 8x \): \(-4y = 16x\) (Incorrect because it should be \(-8x\).)

Bud's Steps:

1. Subtract \( 8x \): \(-4y = -8x + 24\) (Correct)
2. Divide by \(-4\): \( y = 2x + 6 \) (Incorrect result.)

Based on the evaluation, the correct response is: Bob has the correct answer.

Question 3

Solve the equation for x:
\[ 3x + 2b = 6c \]

Steps:

1. Subtract \( 2b \) from both sides:
   \[ 3x = 6c - 2b \]
2. Divide by 3 on both sides:
   \[ x = \frac{6c - 2b}{3} \]
   Which simplifies to:
   \[ x = 2c - \frac{2}{3}b \]

The given process is:
Step 4: \( x = 2c - 2b \) (This part is incorrect; it should have been \( x = 2c - \frac{2}{3}b \).)

Correct Response:
The process has an error. The correct answer is \( x = 2c - \frac{2}{3}b \).

Final Responses

1. Question 1: \( y = \frac{12}{7}x \)
2. Question 2: Bob
3. Question 3: The process has an error. The correct answer is \( x = 2c - \frac{2}{3}b \)