Certainly! Let's break this problem down step-by-step:
1. Identify each part of the expression:
- "Five" is [tex]\(5\)[/tex].
- "More than" indicates addition ([tex]\(+\)[/tex]).
- "The product of two and a number" translates to [tex]\(2 \times a\)[/tex].
- "Decreased by seven" means we subtract [tex]\(7\)[/tex].
2. Write the expression:
Combining these parts, you get:
[tex]\[
5 + (2 \times a) - 7
\][/tex]
3. Substitute the value of [tex]\(a\)[/tex]:
You are given that [tex]\(a = 8\)[/tex]. Substitute [tex]\(8\)[/tex] in for [tex]\(a\)[/tex]:
[tex]\[
5 + (2 \times 8) - 7
\][/tex]
4. Simplify the expression using the order of operations (PEMDAS/BODMAS):
- First, evaluate the multiplication inside the parentheses:
[tex]\[
2 \times 8 = 16
\][/tex]
- Then substitute this value back into the expression:
[tex]\[
5 + 16 - 7
\][/tex]
- Next, perform the addition:
[tex]\[
5 + 16 = 21
\][/tex]
- Finally, complete the subtraction:
[tex]\[
21 - 7 = 14
\][/tex]
Therefore, the answer is:
[tex]\[
\boxed{14}
\][/tex]
