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A slightly different approach to solving equations

Suppose we have the equation 4x + 2 = 18. Normally, we're taught to solve this problem by cancelling out the 2 by subtracting it from itself, and then subtracting this same 2 from the 18, and making it 16. Next, we would normally cancel out the 4x by dividing it by itself, and we would then divide the aforementioned 16 by this 4. Our final answer would be 4. There is nothing wrong with this method, so far as it goes, but there is another way of understanding and solving the equation. First, we do what we normally do and cancel out the two by itself, and then subtract the 18 by the two. Next, we think of the 4x as a fraction, and we multiply the 16 by the 1/4. This provides us with the same answer: 4.