To determine which expression correctly represents the phrase "twice the difference of a number and 5," we will break down the phrase step-by-step:
1. Identify the variable: Let's denote "a number" by the variable [tex]\( x \)[/tex].
2. Difference of a number and 5: The difference between the number [tex]\( x \)[/tex] and 5 can be written mathematically as [tex]\( x - 5 \)[/tex].
3. Twice the difference: To find twice the difference, we multiply the difference [tex]\( x - 5 \)[/tex] by 2. Thus, we have:
[tex]\[ 2 \times (x - 5) \][/tex]
Now, let's compare this expression with the given options:
- [tex]\( -5 + 2x \)[/tex]: This expression does not match our derived expression. It represents adding 2 times a number and subtracting 5, which is not what we need.
- [tex]\( 2(x - 5) \)[/tex]: This expression matches what we derived exactly. It represents twice the difference of a number and 5.
- [tex]\( 2 + 2(x - 5) \)[/tex]: This expression represents adding 2 to twice the difference of a number and 5, which does not match the needed form.
- [tex]\( 2(x + 5) \)[/tex]: This expression represents twice the sum of a number and 5, which is different from the difference of a number and 5.
Therefore, the correct expression that represents the phrase "twice the difference of a number and 5" is:
[tex]\[ 2(x - 5) \][/tex]
So, the correct answer is [tex]\( 2 \)[/tex].
