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

  • Thread starter mister_mister3
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In summary, the conversation discusses a math problem involving equilibrium in a grade 12 chemistry course. The equation is simplified by getting rid of the fraction and then solving for x by getting it alone on one side. The steps involve using opposite operations such as adding, subtracting, multiplying, and dividing to isolate x. The answer for x is 0.56.
  • #1
mister_mister3
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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!
 
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  • #2
(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).
 
  • #3
math

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

1. What is the purpose of solving (2.5 + 2x) / (2.0 - x) = 2.50 equation in Grade 12 Chem Course?

The purpose of solving this equation is to understand the relationship between reactants and products in a chemical reaction, and to determine the amounts of each substance involved in the reaction.

2. How does solving this equation relate to chemistry?

In chemistry, equations are used to represent chemical reactions and the changes in the amounts of substances involved. By solving this equation, we can determine the exact amounts of reactants and products present in a chemical reaction.

3. What is the process of solving (2.5 + 2x) / (2.0 - x) = 2.50 equation?

The process involves simplifying the equation, isolating the variable, and solving for its value. This can be done through various algebraic manipulations, such as combining like terms, cross-multiplying, and isolating the variable on one side of the equation.

4. What are the key concepts required to solve this equation?

To solve this equation, one must have a strong understanding of algebraic concepts such as solving equations with multiple variables, manipulating fractions, and using the distributive property. Knowledge of basic chemistry principles, such as stoichiometry and balancing equations, is also necessary.

5. What are some real-world applications of solving (2.5 + 2x) / (2.0 - x) = 2.50 equation?

This type of equation is commonly used in chemistry to determine the quantities of substances needed for a reaction. It can also be applied in other fields, such as engineering, to calculate the amounts of materials needed for a desired outcome.

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