Sure, let's break down the problem step-by-step.
1. Analyze the given phrase: "Four times a number increased by seven."
2. Identify keywords and their mathematical meaning:
- "Four" corresponds to the number [tex]\( 4 \)[/tex].
- "Times" indicates multiplication ([tex]\( \times \)[/tex]).
- "A number" will be represented by the variable [tex]\( n \)[/tex].
- "Increased by" indicates addition ([tex]\( + \)[/tex]).
- "Seven" corresponds to the number [tex]\( 7 \)[/tex].
3. Translate the phrase into a mathematical expression:
- Start with "four times a number":
[tex]\( 4 \times n \)[/tex] or simply [tex]\( 4n \)[/tex] (since in algebra, multiplication between a number and a variable is written without the multiplication sign).
- Then, "increase by seven":
[tex]\( 4n + 7 \)[/tex].
So, the mathematical expression for "Four times a number increased by seven" is:
[tex]\[ 4n + 7 \][/tex]
4. Check the operations involved:
- Multiplication and addition are used in [tex]\( 4n + 7 \)[/tex].
- Multiplication and subtraction are not used in this context.
Thus, the correct expression is:
[tex]\[ 4n + 7 \][/tex]
Notably, the expression [tex]\( 4n - 7 \)[/tex] does not apply to the description "increased by seven" but would apply to "decreased by seven."
So, the expression should be written as [tex]\( 4n + 7 \)[/tex].
