Solve the equation and check the solution.

Question

-5(t-6)-(t+8)=2

The solution is t= what ? (Type an integer or simplified fraction.)

Answer 1

Step 1. get rid of the parentheses.  We'll do one at a time to avoid confusion.  First factor in the -5 into the (t-6) by multiplying like this:

(-5)(t) - (-5)(6)

-5t - (-30)                 

-5t + 30

So -5(t-6) - (t+8) = 2 changes to

-5t+30 - (t+8) = 2                          (take notice how the plus and minus signs appear because of the -5)

Now do the same for the - (t+8)

Take note how the negative is in from of the parentheses.  This is like saying

-1*(t+8)

Doing this long ways to avoid errors will look like this:

(-1)(t) + (-1)(8) = -t - 8

Now plug this into the expression and we now have:

-5t+30 - t - 8  = 2

Step 2 simplify the left side of the expression by rearranging and  adding all the "like" values together.  For instance:

Add real numbers together: 30 - 8

Add numbers with "t" together: -5t - t

The expression will look like this:

Step a)  -5t - t + 30 - 8 = 2

Step b)  -6t + 22 = 2

Now you want to get the unknown value by itself.  I prefer to keep unknowns like t to the left so subtract out the 22 from both sides like this:

-6t + 22-22 = 2-22

this will give us

-6t = -20

Now we need to separate t by dividing both sides by -6 like this:

-6t/-6 = -20/-6

and the answer is now

t = -20/-6

Simplify further by canceling the negatives:

t = 20/6

and even further if needed by doing the actual division:

t = 3 2/6 which reduces to 3 1/3

Make sense?