 Suppose you make a mistake when simplifying the first step. Let's look at what could happen. Have a look at this example: 2(3x + 1) + 4 = 11 Let's solve it: 6x + 1 + 4 = 11 You can see that a mistake was made in the very first step. The 2 was multiplied by the 3x, but not the 1. Let's continue to solve. No more mistakes will be made. 6x + 1 + 4 = 11 6x + 5 = 11 6x + 5 - 5 = 11 - 5 6x = 6 x = 1 Now suppose we choose to check this answer in the third line : 6x + 5 = 11 The check would certainly be less work using this line. Here goes: 6x + 5 = 11 6(1) + 5 = 11 6 + 5 = 11 11 = 11 The check worked, so we're satisfied our answer was correct. BUT WAIT A MOMENT... we know we made an error and 1 cannot be the correct answer! What happened? Everything we did after the second line was correct. So if we check in any of those lines, the check will work. Only if we check our answer in a line before we made the error will the check not work out. Here's the check using the original equation, before we made the error: 2(3x + 1) + 4 = 11 2(3[1] + 1) + 4 = 11 2(3 + 1) + 4 = 11 2(4) + 4 = 11 8 + 4 = 11 12 = 11 Error detected ... 1 can't be the answer. Since you can never know in which line of your solution there might be an error, the only way to know for certain there are no mistakes is to check your answer in the original question. Incidentally, for word problems, this will mean checking your solution in the words of the question, not the equation which you translated them to. This is especially important for physics problems. |