Solving (2.5 + 2x) / (2.0 - x) = 2.50 Equation in Grade 12 Chem Course

[mister_mister3]

I apologize, but I don't really know what this type of math qualifies as, so it's in general math. Anyhow, it's math that's being used for equilibrium problems in a grade 12 chem course, but my math is VERY rusty...

(2.5 + 2x) / (2.0 - x) = 2.50

and X = 0.56 (sorry, I wasn't sure how to use latex)

My question is this - how do you do the actual calculations, step by step? I'm not even sure what to call this problem to search for it on the internet. I need to know how to manipulate these though, so I may as well become familiar with them.

Any help or links to good sites would be greatly appreciated!

 

[HallsofIvy]

(2.5 + 2x) / (2.0 - x) = 2.50

The first thing you do is simplify the equation by getting rid of the fraction: multiply both sides by (2.0- x) (As long as you do the same (legal) thing on both sides of the equation you will get an "equivalent equation"- one that is true if and only if the first is). Multiplying the left side by (2.0-x) just cancels the denominator of the fraction and you get 2.5+ 2x= 2.5(2.0-x) so 2.5+ 2x= 5.0- 2.5x.

Now get x alone on one side. To get x alone on the left side only, I need to get rid of that "2.5" added on the left side and I need to get rid of that 2.5x subtracted on the right. The "opposite" of adding 2.5 is subtracting 2.5 so "subtract 2.5 from both sides: Of course 2.5- 2.5= 0 so 2.5+ 2x- 2.5= 2x: we get just 2x on the left. On the right we have 5.0- 2.5x- 2.5= 2.5- 2.5x. Now our equation reads 2x= 2.5- 2.5x.
The "opposite" of subtracting 2.5x is adding 2.5x so we add 2.5x to both sides:
2x+ 2.5x= 2.5- 2.5x+ 2.5x which is just 4.5x= 2.5.
Now the only reason x is not alone on the left is because it is multiplied by 4.5. The "opposite" of multiplying by 4.5 is dividing by 4.5 so divide both sides by 4.5:
(4.5x)/4.5= 2.5/4.5 or x= 0.555... (Since you numbers involved 2 significant figures, you were round to 0.56).

 

[mister_mister3]

math

Thanks a lot for the help, everything's clear now!