To determine the value of the expression \(-3mn + 4m - 3\) given that \(m = 2\) and \(n = -4\), follow these steps:
1. Substitute the values of \(m\) and \(n\) into the expression.
2. Simplify the expression by performing the appropriate arithmetic operations.
Given:
[tex]\[ m = 2 \][/tex]
[tex]\[ n = -4 \][/tex]
Substituting these values into the expression \(-3mn + 4m - 3\):
[tex]\[ -3(2)(-4) + 4(2) - 3 \][/tex]
Step-by-Step Calculations:
1. Calculate the product \(2 \cdot -4\):
[tex]\[ 2 \cdot -4 = -8 \][/tex]
2. Substitute \(-8\) into the expression:
[tex]\[ -3(-8) + 4(2) - 3 \][/tex]
3. Calculate \(-3 \cdot -8\):
[tex]\[ -3 \cdot -8 = 24 \][/tex]
So the expression now reads:
[tex]\[ 24 + 4(2) - 3 \][/tex]
4. Calculate the product \(4 \cdot 2\):
[tex]\[ 4 \cdot 2 = 8 \][/tex]
So the expression now reads:
[tex]\[ 24 + 8 - 3 \][/tex]
5. Perform the addition \(24 + 8\):
[tex]\[ 24 + 8 = 32 \][/tex]
So the expression now reads:
[tex]\[ 32 - 3 \][/tex]
6. Finally, subtract 3 from 32:
[tex]\[ 32 - 3 = 29 \][/tex]
Thus, the value of \(-3mn + 4m - 3\) when \(m = 2\) and \(n = -4\) is:
[tex]\[ \boxed{29} \][/tex]
