Which of the following equations is equivalent to 8 – 0.02x = 2.23x + 3.5?
A) 8 = 2x + 223x + 35
B) 80 – 2x = 223x + 35
C) 800 – 20x = 223x + 35
D) 800 – 2x = 223x + 350

D
Step-by-step explanation:

Keep in mind: In algebra, if one side of the equals sign is modified, the other side must be modified the same as-well.

The only answer in which all numbers were multiplied by the same factor (100) was D. If you look at any number or coefficient in the equation, and compare it to what it equaled in the original equation, you can plainly see what it was multiplied by to change from the original equation. In this case, C is incorrect because when we look at 800, we know that in the original equation it was 8, so it was multiplied by a factor of 100. So, that means the other numbers in the original equation must also be multiplied by a factor of 100. However, when looking at C, we can see that when 0.02x is multiplied by 100, it does not equal 2x as every consecutive factor of 10 moves the decimal place once to the left, and since 100 is 10 * 10, the decimal would only move twice to the left. So 0.02x would change to 2x.
Repeat with the rest, and D comes out to be the right answer.

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