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Solve this equation for y: 4y=3x (1 point) Responses y = 4/3 x y = 4/3 x y = ¾ x y = ¾ x y = 12x y = 12x 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 The process has an error from step 3 to step 4

1 answer

Let's start by solving the first equation for \( y \).

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

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

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

This can also be expressed as:

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

So the correct response is:

  • \( y = \frac{3}{4}x \)

Question 2: Analyze the process of solving \( 2x + b = c \).

The steps given are:

  1. \( 2x + b - b = c - b \)
  2. \( 2x = c - b \)
  3. \( 2x - 2 = c - b - 2 \)
  4. \( x = \frac{c}{2} - \frac{b}{2} - 1 \)

Let's evaluate each step:

Step 1: Correctly subtracting \( b \) from both sides.

  • This step is correct.

Step 2: Simplifying the equation to isolate \( 2x \).

  • This step is also correct.

Step 3: Trying to move from \( 2x = c - b \) to a new equation \( 2x - 2 = c - b - 2 \).

  • This step introduces an error because it inaccurately manipulates the equation. You can only subtract the same value from both sides, and subtracting 2 from \( 2x \) without doing the same to the \( c-b \) side is incorrect.

Step 4: Therefore, this step is based on the previous error and is incorrect.

Conclusion:

  • The answers regarding the correctness of 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

Thus, the correct true statements from the given options are:

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

The other choices stating there is no error in the entire process are false.