To solve the expression [tex]\( -3mn + 4m - 3 \)[/tex] when [tex]\( m = 2 \)[/tex] and [tex]\( n = -4 \)[/tex], we will follow a step-by-step approach, substituting the given values into the expression and simplifying it.
Given values:
[tex]\[ m = 2 \][/tex]
[tex]\[ n = -4 \][/tex]
Now, substitute [tex]\( m \)[/tex] and [tex]\( n \)[/tex] into the expression [tex]\( -3mn + 4m - 3 \)[/tex]:
[tex]\[
-3(2)(-4) + 4(2) - 3
\][/tex]
First, calculate the product [tex]\( -3 \times 2 \times -4 \)[/tex]:
[tex]\[
-3 \times 2 = -6
\][/tex]
[tex]\[
-6 \times -4 = 24
\][/tex]
Next, calculate the term [tex]\( 4 \times 2 \)[/tex]:
[tex]\[
4 \times 2 = 8
\][/tex]
Now add these results and simplify:
[tex]\[
24 + 8 - 3 = 29
\][/tex]
Therefore, the value of the expression [tex]\( -3mn + 4m - 3 \)[/tex] when [tex]\( m = 2 \)[/tex] and [tex]\( n = -4 \)[/tex] is [tex]\( 29 \)[/tex].
Thus, the correct answer is:
[tex]\[
\boxed{29}
\][/tex]
