15. Solve this equation for y: 4y=3x

Question

(1 point)
Responses

y = 4/3 x
y = 4/3 x

y = 2x -4
y = 2x -4

y = 12x
y = 12x

y = ¾ x
y = ¾ x
Question 2
16. Solve the equation for x: 2x+b=c

Check this process:

Step 1: 2x+b−b=c−b

Step 2: 2x=c−b

Step 3: 2x−2=c−b−2

Step 4: x=c2−b−2

Check all of the choices that are true statements.

(2 points)
Responses

There is no error in the process.
There is no error in the process.

The process has an error from step 1 to step 2
The process has an error from step 1 to step 2

The process has an error from step 2 to step 3
The process has an error from step 2 to step 3

The process has an error from step 3 to step 4
The process has an error from step 3 to step 4
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Answer 1

Question 1: Solve for \( y \) in the equation \( 4y = 3x \)

To isolate \( y \), divide both sides of the equation by 4:

\[ y = \frac{3x}{4} \]

This simplifies to:

\[ y = \frac{3}{4}x \]

So the correct response is:

y = ¾ x

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Question 2: Check the process for solving the equation \( 2x + b = c \)

Let's go through each step to identify any errors:

Step 1: \( 2x + b - b = c - b \)

This step is correct. Subtracting \( b \) from both sides maintains balance.

Step 2: \( 2x = c - b \)

This step is also correct, as \( b \) cancels on the left-hand side.

Step 3: \( 2x - 2 = c - b - 2 \)

This step introduces an error. The correct operation would be to divide both sides by 2 instead of subtracting 2. The correct transition should be:

\[ 2x = c - b \implies x = \frac{c - b}{2} \]

So there is an error between Step 2 and Step 3.

Step 4: \( x = \frac{c}{2} - b - 2 \)

This step further extends the error from the previous step.

Conclusion for Question 2

The true statements about the process are:

• The process has an error from step 2 to step 3
• The process has an error from step 3 to step 4

So you should check the following responses:

• The process has an error from step 2 to step 3
• The process has an error from step 3 to step 4