(3t+1)/5=(t+7)/10+(t-5)/10

Question

I solved this question through the linear equation simplification timing both sides by the least common denominator. 5

Once I did the the result was >

3t+1= 2t+14+2t-10

T= 3

However the real answer is t=0

Where am I going wrong?
How am I supposed to simplify this equation?

Answer 1

(3t+1)/5=(t+7)/10+(t-5)/10

multiply both sides by 10

2(3t+1)=t+7+t-5

6t+2=2t+2
subtract two from each side
6t=2t
subtract 2t from each side
4t=0
t=0

Answer 2

multiply each term by 10 , not 5
2(3t+1) = t+7 + t-5
6t + 2 = 2t + 2
4t = 0
t = 0

Answer 3

Hm, so I am supposed to multiple each side by the largest common factor. Correct

Answer 4

If you have an equation with fractions, multiply each term by the lowest common denominator of those fractions.

Answer 5

Which in this case is 10?

Answer 6

Could you please give me a complex solution like this, so I can quickly reassure my self>

Answer 7

try
(x+4)/2 + 5/3 = (2x-1)/5

you should get x = -116/3

(obviously I did not "plan" the equation to come out nicely, just wrote down some numbers)