To find the value of [tex]\( a \)[/tex] in the given equation [tex]\( 3x + 5y = ax - 4x - by \)[/tex], let's start by rearranging and combining like terms.
First, rewrite the equation:
[tex]\[ 3x + 5y = ax - 4x - by \][/tex]
Next, combine the [tex]\( x \)[/tex] terms and the [tex]\( y \)[/tex] terms on the right-hand side:
[tex]\[ 3x + 5y = (a - 4)x - by \][/tex]
Now, for the equation to be balanced, the coefficients of the corresponding terms on both sides of the equation must be equal. Let's compare the coefficients of [tex]\( x \)[/tex] on both sides:
[tex]\[ 3x = (a - 4)x \][/tex]
This gives us the equation:
[tex]\[ 3 = a - 4 \][/tex]
To solve for [tex]\( a \)[/tex], add 4 to both sides of the equation:
[tex]\[ 3 + 4 = a \][/tex]
[tex]\[ a = 7 \][/tex]
Thus, the value of [tex]\( a \)[/tex] is [tex]\( \boxed{7} \)[/tex].
