Respuesta :
Answer:
Option A.
Step-by-step explanation:
The given equation is
[tex]\dfrac{3}{x-4}=\dfrac{x}{7}[/tex]
Step 1: Multiply both sides by (x-4).
[tex]3=\dfrac{x(x-4)}{7}[/tex]
Step 2: Multiply both sides by 7.
[tex]21=x(x-4)[/tex]
Step 3: Using distributive property.
[tex]21=x^2-4x[/tex]
Step 4: Isolate all terms on one side.
[tex]0=x^2-4x-21[/tex]
Step 5: Find factors by splitting the middle term.
[tex]0=x^2-7x+3x-21[/tex]
[tex]0=x(x-7)+3(x-7)[/tex]
[tex]0=(x-7)(x+3)[/tex]
Step 6: Using zero product property, we get
[tex]x=-3, x=7[/tex]
It means student solved the equation correctly.
Therefore, the correct option is A.
Answer:
A. The student solved the equation correctly.
Step-by-step explanation:
We have been given a student's work to solve the equation [tex]\frac{3}{x-4}=\frac{x}{7}[/tex]. We are asked to chose accurate interpretation of the student's work.
Step 1: Multiply both sides by (x-4).
[tex]\frac{3}{x-4}(x-4)=\frac{x}{7}(x-4)[/tex]
[tex]3=\frac{x(x-4)}{7}[/tex]
Step 2: Multiply both sides by 7.
[tex]3\times 7=\frac{x(x-4)}{7}\times 7[/tex]
[tex]21=x(x-4)[/tex]
Step 3: Distribute x on right ride.
[tex]21=x\cdot x-x\cdot 4[/tex]
[tex]21=x^2-4x[/tex]
Step 4: Subtract 21 from both sides.
[tex]21-21=x^2-4x-21[/tex]
[tex]0=x^2-4x-21[/tex]
Step 5: Factor by splitting the middle term.
[tex]0=x^2-7x+3x-21[/tex]
[tex]0=(x-7)(x+3)[/tex]
Step 6: Use zero product property.
[tex](x-7)=0, (x+3)=0[/tex]
[tex]x=7,x=-3[/tex]
Since student's work is correct, therefore, option A is the correct choice.
