5x - 4 = –2(3x + 2)

Question

This is a function that i cannot figure out, im having a lot of trouble with functions

Answer 1

The goal of an equation like this is to get the x variable by itself on one side of the equals sign and the numbers on the other side of the equals sign.  

There are a few things we can do to accomplish this, but mostly we use inverse operations to "get rid of" things until we have what we want.

 

For example, if the equation simply said x+3=5, the answer must be 2 because that makes sense, but in order to show it's true algebraically we can subtract 3 on both sides (the opposite of adding 3) and get this:

 

x + 3 - 3 = 5 - 3           you may also write it like this:        x + 3 = 5

x + 0 = 2                                                                            -3     -3

x = 2                                                                                    x = 2

 

Remember that whatever you do on one side, you need to do on the other side as well, or it won't be equal any more.

 

For your equation, since one of our x's is trapped in the parentheses the first thing we'll want to do is to get rid of those parentheses by distributing the -2 out front.  (This isn't an inverse operation, but it helps us get what we want)

 

5x - 4 = (-2)(3x) + (-2)(2)

5x - 4 = -6x - 4

 

Now we have x's on both sides and number on both sides.  To move them (or get rid of them) we need to use addition and subtraction.  For example, if we want to get ride of that -6x we would have to add 6x to both sides since that's the opposite of it.

 

  5x - 4 = -6x - 4

+6x         +6x

 

11x - 4 = -4

 

Now all the x's are together on the left side and we want to get the numbers together on the right side.  Since there's a minus 4 near the x, we want to add 4 on both sides to get rid of it.  This one's a little tricky because there's a minus 4 on both sides, but that's ok.

 

11x - 4  = -4

       +4 = +4

      11x = 0

 

All of our numbers went away, but we can still complete our equation by getting x alone.  Since the 11 and x are multiplying, we want to divide both sides by 11 to get rid of it.

 

11x = 0

11      11

 

x = 0

 

If you plug this answer back into the original equation, you should see that it checks out.

 

5(0) - 4 = -2 (3(0) + 2)

-4 = -2(2)

-4 = -4

 

Sorry for writing such a long answer, but hopefully it helps in the future as well!