today in class we were working on Abosluote Value Equations and i need help with these

3. one half absolute value 3c+5=6c+4

$$\\3.\\\\
\frac{1}{2}|3c+5|=6c+4\\\\
|3c+5|=2(6c+4)\\\\
2(6c+4)=|3c+5|\\\\
12c+8=|3c+5|\\\\
$now it is very similar to question 2$$$

You should be able to have a go at 4 and 5 by yourself now.

Let us know if this is still a problem.  Or put your answer up and we can check it for you :)

Hi Knk98  

1) 2x=5= 3x+4      There are 2 equal sign so you better correct this one.

2) 

4*|3x+4|=4x+8

4*|3x+4|=4(x+2)

|3x+4|=x+2                I have divided both sides by 4

x+2=|3x+4|                Now think for a momement  |6|=|-(6)|   so    |3x+4| = |-(3x+x)|

hence

x+2=3x+4       or      x+2=-(3x+4)

    2= 2x+4      or      x+2= -3x-4

    -2=2x          or        4x+2=-4

    -1=x           or        4x=-6

     x=-1          or          x=-6/4 = -3/2

   x=-1           or          x=3/2

These are the 2 answers.   

on questoin 2 would you not distribute the 4(x+2) and get 4x+8

4*|3x+4|=4x+8

on questoin 2 would you not distribute the 4(x+2) and get 4x+8

It is really good that you are asking questions Knk98.    

It was already 4x+8 at the very beginning.

I saw that the Left hand side (LHS)  was    4*an absolute value experssion.

If I could factor 4 out of the RHS then I could divide both sides by 4 and the 4s would just go away makeing the equation more simple.

4*|3x+4|=4x+8

4*|3x+4|=4*(x+2)      Now I can divide both sides by 4

$$\\\frac{4*|3x+4|}{4}=\frac{4*(x+2)}{4} \\\\
$Now the 4s can cancel out$\\\\
\frac{\not{4}*|3x+4|}{\not{4}}=\frac{\not{4}*(x+2)}{\not{4}} \\\\
$This will leave me with$\\\\
|3x+4|=x+2\\\\
$I like to swap sides here but it is not really necessary$\\\\
x+2=|3x+4|\\\\
$Now remember how $|2|=|-2|\;\;\; well\\\\
|3x+4|=|-(3x+4)| \qquad too.\\\\
so\\
3x+4=x+2\qquad or \qquad 3x+4=-(x+2)\\\\$$

I finished it before.

If you have any more questions please ask and I will try to explain some more.

It is possible that your real problem is not with absolute equations but just with equations in general.

It is important that you try to isolate the source of your problems then you will know what you need to work on.      

Thanks this really helped me... Now i know what im doin Thanks Melody

Solve    | x²– 4x – 5 | = 7

 | x²– 4x – 5 | = 7

x²– 4x – 5  = +7    OR      x²– 4x – 5  = -7

x2– 4x – 12 = 0     OR      x2– 4x +2 = 0

Now use the quadratic formula with each one to get the answers.  There are 4 answers :)