First, let's break down the problem step by step.
1. Identify the expressions involved:
- We need to find the difference between [tex]\(16p\)[/tex] and [tex]\(15p\)[/tex].
- After finding this difference, we need to subtract 3 from it.
- Finally, we will set this expression equal to [tex]\(\frac{1}{2}\)[/tex].
2. Calculate the difference between [tex]\(16p\)[/tex] and [tex]\(15p\)[/tex]:
[tex]\[
16p - 15p = p
\][/tex]
3. Subtract 3 from this difference:
[tex]\[
p - 3
\][/tex]
4. Set this expression equal to [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[
p - 3 = \frac{1}{2}
\][/tex]
5. Solve for [tex]\(p\)[/tex]:
To isolate [tex]\(p\)[/tex], add 3 to both sides of the equation:
[tex]\[
p - 3 + 3 = \frac{1}{2} + 3
\][/tex]
Simplify the right side:
[tex]\[
p = \frac{1}{2} + 3
\][/tex]
Convert 3 to a fraction to add it easily to [tex]\(\frac{1}{2}\)[/tex]:
[tex]\[
3 = \frac{6}{2}
\][/tex]
So,
[tex]\[
p = \frac{1}{2} + \frac{6}{2}
\][/tex]
Add the fractions:
[tex]\[
p = \frac{1 + 6}{2} = \frac{7}{2}
\][/tex]
6. Solution:
The value of [tex]\(p\)[/tex] that satisfies the equation is:
[tex]\[
p = \frac{7}{2}
\][/tex]
To summarize:
- The difference [tex]\(16p - 15p\)[/tex] gives us [tex]\(p\)[/tex].
- Subtracting 3 from [tex]\(p\)[/tex] gives us [tex]\(p - 3\)[/tex].
- Setting [tex]\(p - 3\)[/tex] equal to [tex]\(\frac{1}{2}\)[/tex] and solving for [tex]\(p\)[/tex] gives us [tex]\(p = \frac{7}{2}\)[/tex].
Thus, the solution is [tex]\(p = \frac{7}{2}\)[/tex].
