Final answer:
None of the options (A, B, C, D) provided in the multiple-choice question are equivalent to the equation 4x + 7y = z. Correct solutions would be x = (z - 7y) / 4 or y = (z - 4x) / 7. So, the correct answer is C. x =(z-7y).
Step-by-step explanation:
The student has asked which option is equivalent to the equation 4x + 7y = z.
To find the equivalent form, we need to solve for one of the variables in terms of the others.
Option A: x = 4z - 28y is not correct because if we isolate x in the original equation by subtracting 7y from both sides and then dividing by 4, we get x = (z - 7y)/4.
Option B: y = 7z + 28x is not correct because on isolating y in the original equation by subtracting 4x from both sides and then dividing by 7, we get y = (z - 4x)/7.
Option C: x = (z - 7y) is correct if '4' is added to the denominator, making the correct expression x = (z - 7y) / 4.
Option D: y = (z + 4x) can be the correct expression only if the terms are divided by '7', yielding the correct expression y = (z - 4x) / 7.
Therefore, none of the options provided are equivalent to 4x + 7y = z in their current form.
So, the correct answer is C. x =(z-7y).