Answer :

To solve the inequality [tex]\( f - 35 < -89 \)[/tex], follow these steps:

1. Add 35 to both sides: This will isolate the variable [tex]\( f \)[/tex] on the left side of the inequality. By performing the same operation on both sides, the inequality will be balanced.

[tex]\[
f - 35 + 35 < -89 + 35
\][/tex]

2. Simplify the expression: The left side simplifies to [tex]\( f \)[/tex]. On the right side, calculate [tex]\(-89 + 35\)[/tex].

[tex]\[
f < -54
\][/tex]

So, the solution to the inequality is [tex]\( f < -54 \)[/tex].