Question

How do you solve `(x-3)/(5)+(2x+1)/(4)=6/(10)`?

Answer 1

The solution is `x= 19/14`.

The procedure is as follows:
First, you have to make a common denominator for both members of the equation. The minimum common multiplier of 5, 4 and 10 is 20. So you write the equation as `(4(x-3))/20 + (5(2x+1))/20 = (2·6)/20`, and then, operating, you obtain: `(4x-12)/20 + (10x+5)/20 = 12/20`. And operating the similar terms you obtain: `(14x-7)/20 = 12/20`.
Now you must work only with the numerators making: `14x-7=12 => 14x= 19 => x=19/14`.