To demonstrate whether the inequality [tex]\( 18f - 36 \neq 36 - 18f \)[/tex] holds true, let's evaluate both sides of the inequality.
1. Expression on the Left-Hand Side (LHS):
[tex]\[
\text{LHS} = 18f - 36
\][/tex]
2. Expression on the Right-Hand Side (RHS):
[tex]\[
\text{RHS} = 36 - 18f
\][/tex]
Now, let's test this inequality with a specific value for [tex]\( f \)[/tex]. Let’s use [tex]\( f = 1 \)[/tex] as a simple test case.
1. Substituting [tex]\( f = 1 \)[/tex] into the LHS:
[tex]\[
\text{LHS} = 18(1) - 36 = 18 - 36 = -18
\][/tex]
2. Substituting [tex]\( f = 1 \)[/tex] into the RHS:
[tex]\[
\text{RHS} = 36 - 18(1) = 36 - 18 = 18
\][/tex]
Comparing the evaluated results:
[tex]\[
\text{LHS} = -18
\][/tex]
[tex]\[
\text{RHS} = 18
\][/tex]
Therefore, the LHS is [tex]\(-18\)[/tex] and the RHS is [tex]\(18\)[/tex].
Since [tex]\(-18 \neq 18\)[/tex], the inequality [tex]\( 18f - 36 \neq 36 - 18f \)[/tex] holds true for [tex]\( f = 1 \)[/tex].
Hence, we can conclude that the inequality is verified for this case because:
[tex]\[
-18 \neq 18
\][/tex]
Thus, the statement [tex]\( 18f - 36 \neq 36 - 18f \)[/tex] is true.
