To determine which expression represents the phrase "twice the difference of a number and 5," we need to translate this phrase into a mathematical expression. Let's break down the phrase step by step:
1. Identify the unknown number: Let's call the unknown number [tex]\( x \)[/tex].
2. Find the difference of the number and 5: This can be written as [tex]\( x - 5 \)[/tex].
3. Twice the difference: Multiply the difference [tex]\( x - 5 \)[/tex] by 2.
Putting these steps together, we get the expression:
[tex]\[
2 \cdot (x - 5)
\][/tex]
Now, let's distribute the multiplication:
[tex]\[
2 \cdot (x - 5) = 2 \cdot x - 2 \cdot 5 = 2x - 10
\][/tex]
Therefore, the expression that represents "twice the difference of a number and 5" is:
[tex]\[
2(x - 5)
\][/tex]
To verify against the given options:
- [tex]\(2(x-5)\)[/tex]
- [tex]\(2(x+5)\)[/tex]
- [tex]\(-5 + 2x\)[/tex]
- [tex]\(2 + 2(x-5)\)[/tex]
The correct option is:
[tex]\[
2(x-5)
\][/tex]
