SOLUTION: Can you please help me with this problem? I need to solve for x. 6x-2 / 3 + x-3 / 2 = 1/5

Question 480564: Can you please help me with this problem? I need to solve for x.
6x-2 / 3 + x-3 / 2 = 1/5
Answer by Maths68(1474) (Show Source): You can put this solution on YOUR website!
6x-2 / 3 + x-3 / 2 = 1/5
Taking LCM 3 and 2 which is 6 so multiply by 6 both sides
6(6x-2 / 3) + 6(x-3 / 2) =6(1/5)
2(6x-2) + 3(x-3) = 6/5
12x-4+3x-9=6/5
15x-13=6/5
Add 13 both sides of the equation
15x-13+13=6/5+13
15x=(6+65)/5
15x=71/5
Divide by 15 both sides
15x/15=(71/5)/15
x=(71/5)(1/15)
x=71/75
Check
6x-2 / 3 + x-3 / 2 = 1/5
Put the value of x in above equation
[6(71/75)-2]/3+[(71/75)-3]/2=1/5
[(426/75)-2]/3+[(71/75)-3]/2=1/5
[(426-150)/75]/3+[(71-225)/75]/2=1/5
[(276/75)/3]-[(154)/75]/2=1/5
(276/75)*(1/3)-(154/75)*(1/2)=1/5
(92/75)-(77/75)=1/5
(92-77)/75=1/5
15/75=1/5
1/5=1/5
Explanation on canceling out /3 and /2
6(6x-2 / 3) + 6(x-3 / 2) =6(1/5)
we can write above expression as follows
or [6(6x-2)/3]+[6(x-3)/2]=6/5
or [6/3(6x-2)]+[6/2(x-3]=6/5
or 2(6x-2) + 3(x-3) = 6/5
I hope it clarifies
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