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
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