SOLUTION: Can you please help me solve this problem? -8(1/4t - 4)= 12 - 2t

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Question 75807: Can you please help me solve this problem?
-8(1/4t - 4)= 12 - 2t

Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!

Can you please help me solve this problem?
Is it this?:
1. -8%281%2F%284t+-+4%29%29=12+-+2t
Or is it this?:
2. +-8%281%2F4t+-+4%29+=+12+-+2t
Or is it this?:
3. +-8%28%281%2F4%29t+-+4%29+=+12+-+2t
When you type an algebra problem all on one line
you have to put parentheses around the denominator
to show whether the denominator consists of just
the 4, the 4t or the 4t-4
-----------------------------------------------
If it's
1. -8%281%2F%284t+-+4%29%29=12+-+2t
then put the right side over 1 so
everythinbg will be a fraction and put parentheses
around it:
-8%281%2F%284t+-+4%29%29=%28%2812+-+2t%29%2F1%29
Find the LCD which is %284t+-+4%29
but put it over one and in parentheses like this:
%28%284t-4%29%2F1%29
Then multiply both sides of the equation by it:
-8%281%2F%284t+-+4%29%29%28%284t-4%29%2F1%29=%28%2812+-+2t%29%2F1%29%28%284t-4%29%2F1%29
Cancel out the %284t-4%29's on the left which just leaves
-8 on the left and erase the 1 denominators on the right
and you just have:
-8+=+%2812-2t%29%284t-4%29
Use FOIL on the right
-8+=+48t+-+48+-+8t%5E2+%2B+8t
Combine terms on the right:
-8+=+56t+-+48+-+8t%5E2
Get 0 on the right:
8t%5E2+-+56t+-+8+%2B+48+=+0
8t%5E2+-+56t+%2B+40=0
Divide everty term by 8
%288t%5E2%29%2F8+-+%2856t%29%2F8+%2B+40%2F8+=+0%2F8
t%5E2+-+7t+%2B+5=0
Solve that by the quadratic formula
a = 1, b = -7, c = 8
t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
t+=+%28-%28-7%29+%2B-+sqrt%28+%28-7%29%5E2-4%2A%281%29%2A%285%29+%29%29%2F%282%2A%281%29%29+

t+=+%287+%2B-+sqrt%2849-20%29%29%2F2+
t+=+%287+%2B-+sqrt%2829%29%29%2F2+
So the answers are
t+=+%287+%2B+sqrt%2829%29%29%2F2+ and t+=+%287+-+sqrt%2829%29%29%2F2+
------------------------
If it's
2. +-8%281%2F4t+-+4%29+=+12+-+2t
then distribute on the left to remove
the parentheses
+-8%281%2F4t%29+-+%28-8%294+=+12+-+2t
+%28-8%2F4t%29+-+%28-32%29+=+12+-+2t
+%28-2%2Ft%29+%2B+32+=+12+-+2t
Put 1 under the 32, 12 and -2t so
everything will be a fraction, and put
parentheses around them
+%28-2%2Ft%29+%2B+%2832%2F1%29+=+%2812%2F1%29+-+%282t%29%2F1
The LCD is t, so put it over 1 as %28t%2F1%29
and multiply every term by it:

We can cancel the t's in the first term and erase
all the 1 denominators and get:
+-2+%2B+32t+=+12t+-+2t%5E2
Get 0 on the right
2t%5E2+%2B20t+-+2+=+0
Divide every term by 2

%282t%5E2%29%2F2+%2B%2820t%29%2F2+-+2%2F2+=+0%2F2
t%5E2+%2B+10t+-+1+=+0
Solve that by the quadratic formula
a = 1, b = 10, c = -1
t+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+


t+=+%28-10+%2B-+sqrt%28100%2B4%29%29%2F2+
t+=+%28-10+%2B-+sqrt%28104%29%29%2F2+
t+=+%28-10+%2B-+sqrt%284%2A26%29%29%2F2+
t+=+%28-10+%2B-+sqrt%284%29sqrt%2826%29%29%2F2+
t+=+%28-10+%2B-+2sqrt%2826%29%29%2F2+
So the answers are
t+=+%28-10+%2B+2sqrt%2826%29%29%2F2+ and t+=+%28-10+-+2sqrt%2826%29%29%2F2+
------------------
If it's
3. +-8%28%281%2F4%29t+-+4%29+=+12+-+2t
then distribute on the left to remove the parentheses
+-8%281%2F4%29t+-+%28-8%29%284%29+=+12+-+2t
-2t+%2B+32+=+12+-+2t
32=12
So there is no solution.
-------------------
Edwin