If `ax-c=bx+d`, what is x in terms of a, b, c, and d?

Answer

To solve the equation \( ax - c = bx + d \) for \( x \) in terms of \( a \), \( b \), \( c \), and \( d \), we can follow these steps:

### Step 1: Rearrange the equation
Start with the original equation:
\[ ax - c = bx + d \]
We want to get all terms involving \( x \) on one side and the constant terms on the other side. To do this, we can add \( c \) to both sides and subtract \( bx \) from both sides:
\[ ax - bx = c + d \]

### Step 2: Factor out \( x \)
Now, we can factor \( x \) out of the left side:
\[ (a - b)x = c + d \]

### Step 3: Solve for \( x \)
To isolate \( x \), divide both sides by \( (a - b) \):
\[ x = \frac{c + d}{a - b} \]

### Final Answer
Thus, the value of \( x \) in terms of \( a \), \( b \), \( c \), and \( d \) is:
\[ x = \frac{c + d}{a - b} \]