Let's start by selecting a value for [tex]\( h \)[/tex] that is neither 0 nor 1. For this demonstration, let's choose [tex]\( h = 3 \)[/tex].
1. First, we need to evaluate the left-hand side expression [tex]\( 5h + 2h^2 \)[/tex]:
[tex]\[
5h + 2h^2
\][/tex]
2. Substitute [tex]\( h = 3 \)[/tex] into the expression:
[tex]\[
5(3) + 2(3)^2
\][/tex]
3. Calculate [tex]\( 5(3) \)[/tex]:
[tex]\[
5 \times 3 = 15
\][/tex]
4. Next, calculate [tex]\( 2(3)^2 \)[/tex]:
[tex]\[
2 \times 3^2 = 2 \times 9 = 18
\][/tex]
5. Add the results from steps 3 and 4:
[tex]\[
15 + 18 = 33
\][/tex]
So, the left-hand side [tex]\( 5h + 2h^2 \)[/tex] evaluates to 33 when [tex]\( h = 3 \)[/tex].
Next, let's evaluate the right-hand side expression [tex]\( 7h \)[/tex]:
1. Using the same value [tex]\( h = 3 \)[/tex]:
[tex]\[
7h
\][/tex]
2. Substitute [tex]\( h = 3 \)[/tex] into the expression:
[tex]\[
7(3)
\][/tex]
3. Calculate [tex]\( 7(3) \)[/tex]:
[tex]\[
7 \times 3 = 21
\][/tex]
So, the right-hand side [tex]\( 7h \)[/tex] evaluates to 21 when [tex]\( h = 3 \)[/tex].
Now, compare the two results:
- Left-hand side: [tex]\( 33 \)[/tex]
- Right-hand side: [tex]\( 21 \)[/tex]
Since [tex]\( 33 \)[/tex] is not equal to [tex]\( 21 \)[/tex], the statement [tex]\( 5h + 2h^2 = 7h \)[/tex] is not true when [tex]\( h = 3 \)[/tex].
Hence, we can conclude that [tex]\( 5h + 2h^2 = 7h \)[/tex] is not a true statement for [tex]\( h = 3 \)[/tex], as the left-hand side (33) does not equal the right-hand side (21).
