Question

solve and check the equation.
\frac{x}{6}=\frac{x}{7}-9
what is the solution? select the correct choice below and, if necessary
a. the solution set is {}.
b. the solution set is {x|x is a real number}.
c. the solution set is ∅.

Explanation:

Step1: Find common - denominator

Multiply each term by 42 (the LCM of 6 and 7) to clear the fractions: $42\times\frac{x}{6}=42\times(\frac{x}{7}-9)$.
This simplifies to $7x = 6x-378$.

Step2: Isolate the variable

Subtract $6x$ from both sides of the equation: $7x - 6x=6x - 378-6x$.
We get $x=-378$.

Step3: Check the solution

Substitute $x = - 378$ into the original equation:
Left - hand side: $\frac{-378}{6}=-63$.
Right - hand side: $\frac{-378}{7}-9=-54 - 9=-63$.
Since the left - hand side equals the right - hand side, the solution is valid.

Answer:

A. The solution set is $\{-378\}$