# How is the following equation solved? `(3x)/2 - (x+1)/3 = -1/5` It's a multiple choice question, and one of the choices is 45x-10x+10=-1, but to me, it should read 45x-10x-10=-1 Which is right?...

How is the following equation solved?

`(3x)/2 - (x+1)/3 = -1/5`

It's a multiple choice question, and one of the choices is 45x-10x+10=-1, but to me, it should read 45x-10x-10=-1

Which is right?

Thank you!

durbanville | High School Teacher | (Level 2) Educator Emeritus

Posted on

The equation: `(3x)/2-(x+1)/3=-1/5`

can go through various stages in the process of solving. Neither of the above possible solutions would work, although both of them have some of the correct elements:

To remove the denominator, multiply everything by 30 (the LCD) `30 divide 2=15, 30 divide 3=10 and 30 divide 5=6`

`therefore (3x)/2-(x+1)/3=-1/5`  becomes  `15(3x)-10(x+1)=6(-1)` remembering that everything in the equation is affected by the change (ie both sides)

`therefore 45x-10x-10=-6` . So you were right about the symbol change  (-) but don't forget the right hand side.

Ans:

45x-10x-10=-6 goes on to solve as x=`4/35`

Sources:

steveschoen | College Teacher | (Level 1) Associate Educator

Posted on

Hi, teebs.

I'm not sure what you mean by solved.  It looks like we would be looking to find what the first step would give us.  And, judging by what you are showing, it looks like we would multiply everything by the common denominator, 30, on each side.  So:

30*3x/2 - 30(x+1)/3 = 30*(-1/5)

reducing to

45x - 10(x+1) = -6

So, we would have

45x - 10x - 10 = -6

So, honestly, I don't see either one correct.  I see this.  I have your left side.  But, I believe your right side would be -6, not -1.

Sorry, teebs.  I hope this helps.

Till Then,

Steve