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Which expression represents the phrase "twice the difference of a number and 5"?

A. [tex]\(-5 + 2x\)[/tex]
B. [tex]\(2(x - 5)\)[/tex]
C. [tex]\(2 + 2(x - 5)\)[/tex]
D. [tex]\(2(x + 5)\)[/tex]


Sagot :

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].
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