To solve the given equation for [tex]\(h\)[/tex], we will isolate [tex]\(h\)[/tex] on one side of the equation. Here are the steps:
1. Start with the given equation:
[tex]\[
(5 - 3)p = 4h + 2p
\][/tex]
2. Simplify the left-hand side first:
[tex]\[
2p = 4h + 2p
\][/tex]
3. Next, we need to isolate [tex]\(h\)[/tex]. To do that, we subtract [tex]\(2p\)[/tex] from both sides of the equation:
[tex]\[
2p - 2p = 4h + 2p - 2p
\][/tex]
4. This simplifies to:
[tex]\[
0 = 4h
\][/tex]
5. Now, divide both sides by 4 to solve for [tex]\(h\)[/tex]:
[tex]\[
\frac{0}{4} = \frac{4h}{4}
\][/tex]
6. Simplifying this gives:
[tex]\[
0 = h
\][/tex]
So, the solution for [tex]\(h\)[/tex] is:
[tex]\[
h = 0
\][/tex]
This shows that [tex]\(h\)[/tex] must be zero to satisfy the original equation. Additionally, the simplified form of the initial equation:
If we write the equation in a standard linear form related to [tex]\(h\)[/tex]:
[tex]\[0 = -4h\][/tex]
Here, the expression simplifies to:
[tex]\[
-4h
\][/tex]
Therefore, the complete solution shows that:
The simplified version of the equation is [tex]\(-4h = 0\)[/tex], and the solution for [tex]\(h\)[/tex] is [tex]\(h = 0\)[/tex].
