Question

solve and check the equation.
\\(\frac{x}{12} = \frac{x}{13} - 12\\)

what is the solution? select the correct choice below and, if necessary, fill in the answer box to complete your choice.
a. the solution set is \\(\square\\)

b. the solution set is \\{x | x is a real number\\}.

c. the solution set is \\(\varnothing\\).

Explanation:

Step1: Find a common denominator

The common denominator of 12 and 13 is \( 12\times13 = 156 \). Multiply each term by 156 to eliminate the fractions:
\( 156\times\frac{x}{12}=156\times\frac{x}{13}-156\times12 \)

Step2: Simplify each term

Simplify each term:
\( 13x = 12x - 1872 \)

Step3: Solve for x

Subtract \( 12x \) from both sides:
\( 13x - 12x = 12x - 1872 - 12x \)
\( x = - 1872 \)

Step4: Check the solution

Substitute \( x = - 1872 \) into the original equation:
Left - hand side: \( \frac{-1872}{12}=-156 \)
Right - hand side: \( \frac{-1872}{13}-12=-144 - 12=-156 \)
Since the left - hand side equals the right - hand side, \( x=-1872 \) is a valid solution.

Answer:

The solution set is \(\{-1872\}\)