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-6(4-t)=12t

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3 Answers

Hi, Caitlin.

To solve equations like this type, make sure to follow three steps:

1) Simplify both sides of the equation
2) Make sure there is only a variable term (letters) on one side of the equation
3) Think "opposite" - that is, do opposite operations in the opposite order of operations

-6 (4 - t) =  12t

1)  The left side is not simplified.  We can take care of that by distributing the negative 6 to both members of the (   )'s grouping:

-24   +   6t   =  12t

2)  We have variable terms on both sides of the equation.

-24    +   6t   =   12t
         -   6t        - 6t
     -24          =  6t

3) Now think opposite operation on what's preventing the letter from being alone.  The t is being multiplied by 6... so we divide by 6 on both sides:

  -24    =   6t 
    6           6   

    -4  =  t

Or t = -4 to say it "frontwards."

If you are asked to check your answer, put the value of -4 in place of t in the original problem:

-6 (4 - t) = 12t
-6 (4 - (-4)) = 12(-4)
-6 (4 + 4) = 12 • -4
-6 • 8   =  12 • -4
-48   =   -48 

It worked!

Find t. distribute (-6)=(-6*4) - (-6*t) = 12t leaving (-24)-(-6t) = 12t resulting in (-24) + (6t) = 12t isolate t by subtracting 6t from both sides for -24 = 6t divide both sides by 6 t=-4 Substitute -4 for t in the equation. -6(4-t)=12t -6(4-(-4))=12(-4) -6(4+4)=-48 -6(8)=-48 -48=-48 So, it's a solution

So your overall goal is to get t by itself Right?

So, first distribute the -6 :  so mulitply -6*4 and -6*-t  -24+6t=12t

Now move +6t to the other side so the t's are all on the same side, do this by subtracting 6t from both sides: 

-24+6t-6t = 12t-6t. Then simplify:

-24=6t. now let's switch both sides so the t is on the left

6t = -24

now we need to get the t by itself by dividing both sides by 6:

(6t)/is just leaves t because the 6's cancel out and -24/6 is -4

so t=-4