SOLUTION: please could you help me solve this equation: 2x+3 all over 5 - x-2 all over 4 = a half I've tried rearranging and tried making x the subject but all I can get is 8

Algebra ->  Equations -> SOLUTION: please could you help me solve this equation: 2x+3 all over 5 - x-2 all over 4 = a half I've tried rearranging and tried making x the subject but all I can get is 8      Log On


   

Question 551678: please could you help me solve this equation:
2x+3 all over 5 - x-2 all over 4 = a half
I've tried rearranging and tried making x the subject but all I can get is 8 over 3 which doesn't work I don't think?
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
2x+3 all over 5 - x-2 all over 4 = a half
Assume the problem is
%28%282x%2B3%29%29%2F5 - %28%28x-2%29%29%2F4 = 1%2F2
Multiply by 20 to clear the denominators
20*%28%282x%2B3%29%29%2F5 - 20*%28%28x-2%29%29%2F4 = 20*1%2F2
Cancel and you have:
4(2x+3) - 5(x-2) = 10
8x + 12 - 5x + 10 = 10
8x - 5x + 22 = 10
3x = 10 - 22
3x = -12
x = %28-12%29%2F3
x = -4
:
:
Let's see if this works, replace x with -4 in the original equation
%28%282x%2B3%29%29%2F5 - %28%28x-2%29%29%2F4 = 1%2F2
%28%282%28-4%29%2B3%29%29%2F5 - %28%28-4-2%29%29%2F4 = 1%2F2
%28%28-8%2B3%29%29%2F5 - %28%28-6%29%29%2F4 = 1%2F2
%28%28-5%29%29%2F5 - %28%28-6%29%29%2F4 = 1%2F2
-1 - (-3%2F2) = 1%2F2
-1 + 3%2F2 = 1%2F2
-2%2F2 + 3%2F2 = 1%2F2; we can say x=-4 does work