To simplify the expression [tex]\(3(0.5 - p) + 4(p + 0.75)\)[/tex], let's expand and combine like terms.
1. Start by expanding the terms:
[tex]\[
3(0.5 - p) + 4(p + 0.75)
\][/tex]
[tex]\[
= 3 \cdot 0.5 - 3p + 4 \cdot p + 4 \cdot 0.75
\][/tex]
2. Calculate each multiplication:
[tex]\[
= 1.5 - 3p + 4p + 3
\][/tex]
3. Combine like terms:
[tex]\[
= 1.5 + 3 - 3p + 4p
\][/tex]
[tex]\[
= 4.5 + p
\][/tex]
So, the simplified expression is:
[tex]\[
\boxed{4.5 + p}
\][/tex]
Next, we substitute [tex]\(p = 2\)[/tex] into both the given and simplified expressions and evaluate them.
1. Substitute [tex]\(p = 2\)[/tex] into the given expression [tex]\(3(0.5 - p) + 4(p + 0.75)\)[/tex]:
[tex]\[
3(0.5 - 2) + 4(2 + 0.75)
\][/tex]
[tex]\[
= 3(-1.5) + 4(2.75)
\][/tex]
[tex]\[
= -4.5 + 11
\][/tex]
[tex]\[
= 6.5
\][/tex]
So, the value when [tex]\(p = 2\)[/tex] is substituted into the given expression is:
[tex]\[
\boxed{6.5}
\][/tex]
2. Substitute [tex]\(p = 2\)[/tex] into the simplified expression [tex]\(4.5 + p\)[/tex]:
[tex]\[
4.5 + 2
\][/tex]
[tex]\[
= 6.5
\][/tex]
So, the value when [tex]\(p = 2\)[/tex] is substituted into the simplified expression is:
[tex]\[
\boxed{6.5}
\][/tex]
Therefore, both the given expression and the simplified expression yield the same value when [tex]\(p = 2\)[/tex], confirming that they are equivalent expressions.
