Solve the equation and check your solution 2/x+3/2x=7/6

I need help in solving this equation

2/x + 3/2x = 7/6

[2(2) + 3] / 2x = 7/6

7 / 2x = 7 / 6

2x = 6

x = 3

this can be also be. (2/x) + 1/2(3/x) = 7/6
then since the two both have an x in the denominator, you can combine them to be
1/2 ((2+3)/x) = 7/6 which simplifies to 1/2(5/x) = 7/6
then you have to simplify it to solve for x by essentially getting rid of everything on the left side. first multiply both sides by 2 to cancel out the one half.
now you should have (5)/x = 14/6
Now at this point, it's simpler to get the x out of the denominator, so multiply both sides by x. now you have 5 = (14/6)x. It's time to divide 5 by 14/6, but rather than that, you can just flip the fraction and multiply 5 by 6/14 which is the same as if you had divided the original number
so now you figure out that x = 30/14 which simplifies to x = 15/7

2.........3..............7
---..+..---.....=.....---............M… thru by a common denominator of " 6x "
x........2x..............6

6x*2......6x*3............6x*7
------..+..------.....=.....------....… each fraction
...x..........2x.................6

12 + 9 = 7x

21 = 7x

7x = 21
---....----
7.......7

x = 3..........ANSWER

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2/x + 3/(2x) = 7/6

(4 + 3)/2x = 7/6

7/2x = 7/6

2x = 6

x = 3

(4 + 3 ) / 2x = 7/6
14x = 42
=>x = 42/14 = 3

LCD=6X

SO

=6(2)+3(3)=X(7)
=12+9=7X
=21=7X

X=3