A student solved 3/x−4=x/7 in six steps, as shown.

Step 1: 3=x(x−4)/7
Step 2: 21=x(x−4)
Step 3: 21=x**2−4x
Step 4: 0=x**2−4x−21
Step 5: 0=(x−7)(x+3)
Step 6: x=−3, x=7
Which statement is an accurate interpretation of the student's work?

A The student solved the equation correctly.

B The student made an error in step 2.

C The student made an error in step 5.

D Only x=7 is a solution to the original equation.

Option A.

Step-by-step explanation:

The given equation is

Step 1: Multiply both sides by (x-4).

Step 2: Multiply both sides by 7.

Step 3: Using distributive property.

Step 4: Isolate all terms on one side.

Step 5: Find factors by splitting the middle term.

Step 6: Using zero product property, we get

It means student solved the equation correctly.

Therefore, the correct option is A.

A. The student solved the equation correctly.

Step-by-step explanation:

We have been given a student's work to solve the equation . We are asked to chose accurate interpretation of the student's work.

Step 1: Multiply both sides by (x-4).

Step 2: Multiply both sides by 7.

Step 3: Distribute x on right ride.

Step 4: Subtract 21 from both sides.

Step 5: Factor by splitting the middle term.

Step 6: Use zero product property.

Since student's work is correct, therefore, option A is the correct choice.