The Equals Sign

The `=` sign is surely one of the most commonly used symbols in the field of mathematics and other sciences. Its basic meaning isn`t difficult to grasp but is sometimes easily overlooked. For example were you ever taught that when solving an algebraic equation you should group like terms together, and if you have one variable (x, say), to position this on the left of your equation and all the numbers on the right? This is fine. So how do you solve `x + 3 = 5`? Many are taught that you carry the 3 over to the right hand side and the sign changes from + to -. So the equation becomes x = -3 + 5 = 5 - 3 = 2. Millions have memorised this step. It works but does it make sense? Not really. This reasoning ignores the significance of the equals sign. Think of the `=` as a beam balance. For the scale to be balanced you must have weights of equal value on either side. Now with a balance whatever weight you remove on the right must also be removed on the left to maintain equilibrium. The same is true if you want to add weights. Think of x + 3 as the weights on the left. In order to have just the `weight` x on the left you would have to reduce the total value by 3, ie x + 3 - 3, which is x. However, since what you do on one side you must also do on the other to maintain equilibrium, you would also need to remove a weight value of 3 from the right hand side. So you`ll get 5 - 3, which is 2. So here goes: x + 3 = 5 x + 3 - 3 = 5 - 3 x + 0 = 2 x = 2. The same principle works for multiplication, powers, logarithms, and practically every operation.