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

Question

(1 point)
Responses

y = 12x
y = 12x

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

y = ¾ x
y = ¾ x

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

Answer 1

Question 1

To solve the equation \(4y = 3x\) for \(y\):

1. Divide both sides by 4:
   \[ y = \frac{3x}{4} \]
   Alternatively, this can be written as \(y = \frac{3}{4}x\).

The correct answer is y = ¾ x.

Question 2

Let's check the process step-by-step:

1. Step 1:
   \(2x + b - b = c - b\) is correct since we are subtracting \(b\) from both sides.

2. Step 2:
   \(2x = c - b\) is also correct as the \(b\) cancels out on the left side.

3. Step 3:
   The proposed step is \(2x - 2 = c - b - 2\), but this is incorrect. You should not subtract 2 from \(2x\) unless you intend to do so on both sides of the equation.

4. Step 4:
   The final statement \(x = \frac{c}{2} - b - 2\) is also incorrect because of the error made in Step 3.

From the analysis:

• There is no error in the process: False
• The process has an error from step 1 to step 2: False
• The process has an error from step 2 to step 3: True
• The process has an error from step 3 to step 4: True

So, the true statements are:

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