Which of the following algebraic equations models the English sentence, a number decreased by two is equal to four?
A. w + 2 = 4
B. 2 − w = 4
C. w − 2 = 4
D. w = 2 − 4
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To model the English sentence "a number decreased by two is equal to four" as an algebraic equation, we need to understand what each part of the sentence represents:
1. "A number" can be represented by the variable w.
2. "Decreased by two" means subtracting 2 from the number.
3. "Is equal to four" means the result is equal to 4.
Now, let's evaluate each option:
A. w + 2 = 4
This equation represents adding 2 to the number w, not subtracting. So, this option is incorrect.
B. 2 - w = 4
This equation represents subtracting the number w from 2, not subtracting 2 from the number. So, this option is incorrect.
C. w - 2 = 4
This equation represents subtracting 2 from the number w, just as described in the English sentence. So, this option could be the correct answer.
D. w = 2 - 4
This equation represents 2 minus 4, not the number w decreased by 2. So, this option is incorrect.
Based on our analysis, the option that models the English sentence "a number decreased by two is equal to four" is C. w - 2 = 4.