Alright, let's go through the options step-by-step to determine which phrase correctly matches the algebraic expression [tex]\( 2(x + 7) + 10 \)[/tex].
First, consider the given algebraic expression itself:
1. The expression [tex]\( 2(x + 7) \)[/tex] indicates multiplying the entire sum of [tex]\( x \)[/tex] and 7 by 2.
2. Then, we add 10 to the result of [tex]\( 2(x + 7) \)[/tex].
Now, let's examine each phrase to see which one matches the described operations:
1. Two times the sum of [tex]\( x \)[/tex] and seven plus ten:
- This phrase correctly describes first taking the sum of [tex]\( x \)[/tex] and 7.
- Then multiplying this sum by 2.
- Finally, adding 10 to the result.
This matches the structure of the expression [tex]\( 2(x + 7) + 10 \)[/tex].
2. Two times the difference of [tex]\( x \)[/tex] and seven plus ten:
- This phrase would translate to [tex]\( 2(x - 7) + 10 \)[/tex], not [tex]\( 2(x + 7) + 10 \)[/tex].
- Therefore, this phrase is incorrect.
3. Two times [tex]\( x \)[/tex] minus seven plus ten:
- This phrase implies [tex]\( 2x - 7 + 10 \)[/tex], which isn't the same as the given expression.
- Hence, this option is incorrect.
4. Two times [tex]\( x \)[/tex] plus the sum of seven and ten:
- Translating this phrase, we get [tex]\( 2x + (7 + 10) \)[/tex], which simplifies to [tex]\( 2x + 17 \)[/tex].
- This does not match the given expression [tex]\( 2(x + 7) + 10 \)[/tex].
- Therefore, this phrase is also incorrect.
In conclusion, the correct phrase that matches the algebraic expression [tex]\( 2(x + 7) + 10 \)[/tex] is:
Two times the sum of [tex]\( x \)[/tex] and seven plus ten
