Carl Horowitz

**University of Michigan**

Runs his own tutoring company

Carl taught upper-level math in several schools and currently runs his own tutoring company. He bets that no one can beat his love for intensive outdoor activities!

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After learning the definition of a function, we can extend it to define a one to one function. A **one to one function** has not only one output for every input, but also only one input in the domain for every output in therange. Another interesting type is an invertible function, or a function that has an inverse. The graph of a one to one or invertible function has unique and interesting characteristics.

Okay, solving Linear Equations. So solving linear equations is an equation where we basically are solving for a single variable in this case we're going to be talking about x. And so what we really want to do is get that variable by itself just using laws of Math, so properties, addition, subtraction all that good staff.

How I intend to do these problems is simplify each side independently. So here we have a couple of x's throw those together so +2x-8x will leave us with a -6x and we didn't touch the other side so that stays the same, okay. We then want to isolate our variable, so what that means is get all the x's together on one side. We can either bring them to either side it works either way in general I prefer to keep my x's positive so I would add this 6x over you could just as easily subtract that 12 everything works out as well. So you add 6x and -6 will stay there, add 6 to the 12 that will give us 18 and our -4 stays there as well okay. Again trying to get our x by itself so add the 4 over. Add for the both sides add 4, -6+4, -2=18x and to get the x by itself lastly we just divide. Divide by 18, -2 over 18 can be simplified to -1 over 9, and there you go we have solved the simple linear equation.