Questions: When solved for x in terms of a, the solution to the equation 3x-7=ax+5 is A. 12/(3a) B. 12/(3-a) C. 3a/12 D. (3-a)/12

Solution Steps

We start with the equation:

\[ 3x - 7 = ax + 5 \]

Rearranging this equation to isolate terms involving \( x \) gives:

\[ 3x - ax = 5 + 7 \]

This simplifies to:

\[ (3 - a)x = 12 \]

From the equation \( (3 - a)x = 12 \), we can see that the coefficient of \( x \) is \( 3 - a \).

To determine the nature of the solutions, we analyze the coefficient \( 3 - a \):

• If \( 3 - a \neq 0 \), we can solve for \( x \) as follows:

\[ x = \frac{12}{3 - a} \]

• If \( 3 - a = 0 \) (i.e., \( a = 3 \)), the equation becomes \( 0 \cdot x = 12 \), which is inconsistent and has no solutions.

Final Answer