Here's a step-by-step evaluation of each given expression to determine which one is not equivalent to \(72m - 60\):
Expression \(F: \ 6(12m - 10)\)
First, distribute the 6:
[tex]\[
6(12m - 10) = 6 \times 12m - 6 \times 10
\][/tex]
Calculate the multiplication:
[tex]\[
6 \times 12m = 72m
\][/tex]
[tex]\[
6 \times 10 = 60
\][/tex]
Combine these results:
[tex]\[
6(12m - 10) = 72m - 60
\][/tex]
Thus, \(F\) is equivalent to \(72m - 60\).
Expression \(G: \ 4(18m - 15)\)
First, distribute the 4:
[tex]\[
4(18m - 15) = 4 \times 18m - 4 \times 15
\][/tex]
Calculate the multiplication:
[tex]\[
4 \times 18m = 72m
\][/tex]
[tex]\[
4 \times 15 = 60
\][/tex]
Combine these results:
[tex]\[
4(18m - 15) = 72m - 60
\][/tex]
Thus, \(G\) is also equivalent to \(72m - 60\).
Expression \(H: \ 12m\)
This expression is already simplified and does not have a constant term:
[tex]\[
12m
\][/tex]
Clearly, this does not match the given expression \(72m - 60\).
Expression \(I: \ 12(6m - 5)\)
First, distribute the 12:
[tex]\[
12(6m - 5) = 12 \times 6m - 12 \times 5
\][/tex]
Calculate the multiplication:
[tex]\[
12 \times 6m = 72m
\][/tex]
[tex]\[
12 \times 5 = 60
\][/tex]
Combine these results:
[tex]\[
12(6m - 5) = 72m - 60
\][/tex]
Thus, \(I\) is equivalent to \(72m - 60\).
After evaluating all the expressions, we find that the expression \(H: \ 12m\) is not equivalent to the original expression \(72m - 60\).
So, the expression that is not equivalent to the given expression \(72m - 60\) is:
[tex]\[ H. \ 12m \][/tex]
