Answered

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Five more than the product of two and a number, decreased by seven; evaluate when [tex]\( a = 8 \)[/tex]

[tex]\[
\begin{tabular}{|c|c|}
\hline
Key Words & Replace With \\
\hline
five & 5 \\
\hline
more than & + \\
\hline
product & \times \\
\hline
two & 2 \\
\hline
a number & \( a \) \\
\hline
decreased by & - \\
\hline
seven & 7 \\
\hline
\end{tabular}
\][/tex]

Write and evaluate the expression. Then, complete the statements.

1. Write the expression: [tex]\( 5 + 2 \times a - 7 \)[/tex]
2. Substitute [tex]\( a = 8 \)[/tex] into the expression.
3. Simplify using the order of operations.

The answer is [tex]\( \square \)[/tex]

Sagot :

GinnyAnswer
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]
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