Answer :
Sure! Let's go through the problem step by step together:
1. Understand the Problem:
- We have a number, [tex]\( n \)[/tex].
- We're adding this number to "15 less than 3 times itself."
2. Translate to an Equation:
- "3 times itself" means [tex]\( 3n \)[/tex].
- "15 less than 3 times itself" means [tex]\( 3n - 15 \)[/tex].
- We're adding our original number [tex]\( n \)[/tex] to this expression, so we have: [tex]\( n + (3n - 15) \)[/tex].
- The problem states this equals 101, so we write it as: [tex]\( n + (3n - 15) = 101 \)[/tex].
3. Combine Like Terms:
- Simplify the left side of the equation: [tex]\( n + 3n - 15 \)[/tex] becomes [tex]\( 4n - 15 \)[/tex].
4. Form the Simplified Equation:
- The equation now is [tex]\( 4n - 15 = 101 \)[/tex].
5. Select the Correct Equation:
- If we distribute and form the equation from our choices, the setup [tex]\( 3n - 15 + n = 101 \)[/tex] matches our initial expanded form as it rearranges to the same equation after simplifying: [tex]\( 4n - 15 = 101 \)[/tex].
Therefore, the equation that can be used to find the value of [tex]\( n \)[/tex] is:
[tex]\[ 3n - 15 + n = 101 \][/tex]
This is the correct choice among the given options.
1. Understand the Problem:
- We have a number, [tex]\( n \)[/tex].
- We're adding this number to "15 less than 3 times itself."
2. Translate to an Equation:
- "3 times itself" means [tex]\( 3n \)[/tex].
- "15 less than 3 times itself" means [tex]\( 3n - 15 \)[/tex].
- We're adding our original number [tex]\( n \)[/tex] to this expression, so we have: [tex]\( n + (3n - 15) \)[/tex].
- The problem states this equals 101, so we write it as: [tex]\( n + (3n - 15) = 101 \)[/tex].
3. Combine Like Terms:
- Simplify the left side of the equation: [tex]\( n + 3n - 15 \)[/tex] becomes [tex]\( 4n - 15 \)[/tex].
4. Form the Simplified Equation:
- The equation now is [tex]\( 4n - 15 = 101 \)[/tex].
5. Select the Correct Equation:
- If we distribute and form the equation from our choices, the setup [tex]\( 3n - 15 + n = 101 \)[/tex] matches our initial expanded form as it rearranges to the same equation after simplifying: [tex]\( 4n - 15 = 101 \)[/tex].
Therefore, the equation that can be used to find the value of [tex]\( n \)[/tex] is:
[tex]\[ 3n - 15 + n = 101 \][/tex]
This is the correct choice among the given options.
