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when you first learn math you see things like two plus three is equal to five or you might see six plus one is equal to seven or you might see eight minus two is equal to six and all of these you might think that the equal sign just says hey give me the answer figure out what two plus three is two plus three well the answer is five six plus one the enter seven eight minus two the answer is six that's not quite right what the equal sign is saying is that what's on the left side is the same amount the same quantity as what is on the right-hand side it's saying that two plus three is the same thing as five and you didn't have to write it this way you could have written you could have written five is equal to two plus three you could write that three plus two is equal to two plus three notice here we're not figuring out the answer we're just saying that whatever three plus two is that's going to be the same thing as whatever two plus three is we know that they both equal five you could even mix addition and subtraction you could right you could write that six plus one is the same thing is equal to 8 minus one they are the same amount the same quantity what is six plus one well that's seven what's eight minus one well that is seven so the equal sign does not mean just give me the answer just you know add the numbers or subtract the numbers an equal sign is saying that's what's on the left hand side is the same amount as what's on the right hand side so with that in our brain let's write some statements using equal signs some equations you could even say using equal signs and figure out which of them are actually true so if I were to write down if I were to write down I won't even read it out because it might give it away if I were to write down this is this true well the number on the left here is 18 the number on the left is 18 the number on the on the right is a different number it is 81 it is 81 they swap or we swapped the 1 and the 8 they're in different places this is a different number this is 81 these are not equal these are not not equal so this statement is not true and sometimes you might even see someone do something like this that means not equal 18 is not equal to 81 let's keep going what if I were to write what if I were to write 9 minus 3 plus 2 minus 0 is equal to is equal to 0 plus 1 minus 1 plus 8 is this true well let's figure out what the left-hand side is C 9 minus 3 is 6 plus 2 is 8 minus 0 is 8 so this this if I were to if I were to compute it that's equal to 8 and then on the right hand side I have 0 plus 1 minus 1 well 1 minus 1 is 0 so this is all going to be 8 so this is this is true 8 equals 8 this is another way of writing 8 9 minus 3 plus 2 minus 0 this is 8 and this is also 8 so once again the equal sign is just saying that this what we have on the left is the same as what we have on the right let's do another example let's do another example let's do two more examples if I were to write this is this true well you might be tempted a if I put a 1 to the 0 together it's going to look like a 10 but that's not this is not how we do mathematics this is not how we add things 1 plus 0 is just 1 so this would be the same thing as saying the 10 is equal to one which we know is not true so this is not equal this is not equal let's do one more let's say I had 7 plus 1 is equal to 3 plus 4 is this equation true well what do we have on the Left 7 plus 1 is 8 3 plus 4 is 7 these are not the same quantity they're not the same amount so these are not equal and we're done