Let's break down the expression step by step:
1. Identify the components:
- "Seven times a number" can be represented as [tex]\(7x\)[/tex].
- "The sum of seven times a number and five" translates to [tex]\(7x + 5\)[/tex].
- "Negative two times the number" is [tex]\(-2x\)[/tex].
- "The sum of negative two times the number and eleven" is [tex]\(-2x + 11\)[/tex].
2. Combine the components into a fraction as described:
- The part "The sum of seven times a number and five" forms the numerator: [tex]\(7x + 5\)[/tex].
- The part "The sum of negative two times the number and eleven" forms the denominator: [tex]\(-2x + 11\)[/tex].
So the entire expression is:
[tex]\[
\frac{7x + 5}{-2x + 11}
\][/tex]
Now, let's choose the correct phrase from the given options:
1. [tex]\(\frac{-2x + 11}{7x + 5}\)[/tex]
2. [tex]\((-2x + 11) + (7x \div 5)\)[/tex]
3. [tex]\((7x + 5) + (-2x \div 11)\)[/tex]
4. [tex]\(\frac{7x + 5}{-2x + 11}\)[/tex]
The correct answer is:
[tex]\[
(7x + 5) \div (-2x + 11)
\][/tex]
So, the correct phrase is:
[tex]\[
(7 x+5) \div (-2 x+11)
\][/tex]
