To rewrite the expression [tex]\( 0.2 f - 5(7 f + 7) \)[/tex] in its simplest terms, let's follow these steps:
1. Distribute the -5 across the terms inside the parentheses:
[tex]\[
0.2 f - 5(7 f + 7) = 0.2 f - 5 \cdot 7 f - 5 \cdot 7
\][/tex]
Simplifying the multiplications:
[tex]\[
0.2 f - 35 f - 35
\][/tex]
2. Combine the like terms [tex]\(0.2 f\)[/tex] and [tex]\(-35 f\)[/tex]:
[tex]\[
0.2 f - 35 f = (0.2 - 35) f = -34.8 f
\][/tex]
3. Put it all together:
[tex]\[
-34.8 f - 35
\][/tex]
Thus, the simplified form of the given expression is:
[tex]\[
-34.8 f - 35
\][/tex]
