Let's go through the problem step-by-step:
1. Identify Key Words and Their Replacements:
- Four: 4
- Times: × (multiplication)
- A number: [tex]\( n \)[/tex]
- Increased by: + (addition)
- Seven: 7
2. Compose the Expression:
- "Four times a number increased by seven"
- Replace each key phrase with the relevant symbol or number:
- "Four" : 4
- "Times a number" : 4 × [tex]\( n \)[/tex] or simply [tex]\( 4n \)[/tex]
- "Increased by seven" : + 7
Combining these, you get:
- The expression is [tex]\( 4n + 7 \)[/tex]
3. Determine the Operations:
- Multiplication (from "four times a number")
- Addition (from "increased by seven")
Therefore, the expression "Four times a number increased by seven" can be written as:
[tex]\[ 4n + 7 \][/tex]
4. For the verification of other possible forms:
- The expression [tex]\( 4n + 7 \)[/tex] is already derived accurately.
- If you were to consider an expression of subtraction, it would be [tex]\( 4n - 7 \)[/tex], but this does not fit the given phrase "increased by seven".
Summarizing:
- The operations involved in [tex]\( 4n + 7 \)[/tex] are multiplication and addition.
- The expression [tex]\( 4n - 7 \)[/tex] introduces subtraction, which is not relevant in this context.
So, the correct and final expression is:
[tex]\[ 4n + 7 \][/tex]
And the two operations involved are:
1. Multiplication
2. Addition
The expressions and choices outlined:
- The expression is written as: [tex]\( 4n + 7 \)[/tex]
- The expression is not written as: [tex]\( 4n - 7 \)[/tex]
Thus, the accurate statement for this scenario is:
- The expression is written as [tex]\( 4n + 7 \)[/tex].
- The two operations are multiplication and addition.
