To rewrite the equation [tex]\( x + y + 3 = -2x + 4y + 18 \)[/tex] into the general form [tex]\( ax + by + c = 0 \)[/tex], we should follow these steps:
1. Move all terms to one side of the equation:
[tex]\[ x + y + 3 + 2x - 4y - 18 = 0 \][/tex]
2. Combine like terms:
[tex]\[ (x + 2x) + (y - 4y) + (3 - 18) = 0 \][/tex]
[tex]\[ 3x - 3y - 15 = 0 \][/tex]
Thus, the general form of the equation is:
[tex]\[ 3x - 3y - 15 = 0 \][/tex]
Now, let's compare this equation to the provided options:
A. [tex]\( x + y - 5 = 0 \)[/tex]
B. [tex]\( 3x - 3y - 5 = 0 \)[/tex]
C. [tex]\( x - y - 15 = 0 \)[/tex]
D. [tex]\( x - y - 5 = 0 \)[/tex]
The correct answer is B:
[tex]\[ 3x - 3y - 15 = 0 \][/tex]
