Question

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

Answer 1

Answer:

A. The student solved the equation correctly.

Step-by-step explanation:

We have been given a student's work to solve the equation $\frac{3}{x-4}=\frac{x}{7}$. We are asked to chose accurate interpretation of the student's work.

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

$\frac{3}{x-4}(x-4)=\frac{x}{7}(x-4)$

$3=\frac{x(x-4)}{7}$

Step 2: Multiply both sides by 7.

$3\times 7=\frac{x(x-4)}{7}\times 7$

$21=x(x-4)$

Step 3: Distribute x on right ride.

$21=x\cdot x-x\cdot 4$

$21=x^2-4x$

Step 4: Subtract 21 from both sides.

$21-21=x^2-4x-21$

$0=x^2-4x-21$

Step 5: Factor by splitting the middle term.

$0=x^2-7x+3x-21$

$0=(x-7)(x+3)$

Step 6: Use zero product property.

$(x-7)=0, (x+3)=0$

$x=7,x=-3$

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

Answer 2

Answer:

Option A.

Step-by-step explanation:

The given equation is

$\dfrac{3}{x-4}=\dfrac{x}{7}$

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

$3=\dfrac{x(x-4)}{7}$

Step 2: Multiply both sides by 7.

$21=x(x-4)$

Step 3: Using distributive property.

$21=x^2-4x$

Step 4: Isolate all terms on one side.

$0=x^2-4x-21$

Step 5: Find factors by splitting the middle term.

$0=x^2-7x+3x-21$

$0=x(x-7)+3(x-7)$

$0=(x-7)(x+3)$

Step 6: Using zero product property, we get

$x=-3, x=7$

It means student solved the equation correctly.

Therefore, the correct option is A.