Question

A student solved 3/x-4 =x/7 in six steps as shown.Which statement is an accurate interpretation of the students work

Answer 1

Answer:

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^2−4(x)

Step 4: 0=x^2−4(x)−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 is the right choice.

Step-by-step explanation:

Given:

An equation and its step-wise work.

We have to check whether the steps are correct or not.

The equation is:

⇒ $\frac{3}{x-4} = \frac{x}{7}$

Solution:

⇒ $21=x(x-4)$              ...cross multiplying terms.

⇒ $21=x^2-4x$    

⇒ $x^2-4x-21=0$

⇒ $x^2-7x+3x-21=0$ ...using middle term splitting

⇒ $x(x-7)+3(x-7)=0$

⇒ $(x+3)(x-7)$

⇒ $x=-3\ and\ x=7$

The student have solved the question correctly.