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Since I’m starting in the middle of a box vertically, I want to go up to the next middle, up 1 over 2, up 1 over 2.
These facts form the basis of almost all the solving techniques that we’ll be looking at in this chapter so it’s very important that you know them and don’t forget about them. What we do to one side of an equation we have to do to the other side of the equation.
If you remember that then you will always get these facts correct.
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For this problem there are no fractions so we don’t need to worry about the first step in the process. So, we will clear out any parenthesis by multiplying the numbers through and then combine like terms.
\[\begin3\left( \right) & = 2\left( \right) - 2x\ 3x 15 & = - 12 - 2x - 2x\ 3x 15 & = - 12 - 4x\end\] The next step is to get all the \(x\)’s on one side and all the numbers on the other side.This form is sometimes called the standard form of a linear equation.Note that most linear equations will not start off in this form.Let me show you what I did in that pretty amazing 10 seconds. The first thing I did was put this dot right here at down 4 on the y axis.The first thing I did was look to find the y intercept. From there, I counted the slope number which was 3 over 2, so from that dot, I’m going to go up 3 over 2 and make another dot, that’s where this guy came from. From there I just grabbed a ruler and connected them being really careful to extend the line and make arrows on the end to show that it goes on and on towards infinity.The y intercept in this problem is -4, so my first dot on the graph went at -4. So you guys these are like super fast problems if you can get the hang of it. First thing, dot at the y intercept boom, from there count the slope boom, third thing draw the line, forth thing, put the arrows on it.Those are really great problems you guys I think you might even have fun doing your Math homework.Connect the two points and draw arrows at either end to indicate that the line extends infinitely.Here is a problem where I’m asked to graph the equation of the line.In this section we will be solving linear equations and there is a nice simple process for solving linear equations.Let’s first summarize the process and then we will work some examples.