9/8=15/3x+4

Question

What is the correct way to solve this problem?

Answer 1

Hi Michelle,

 

First, I want to confirm that your problem is presented accurately. I'm assuming that the right-hand side of the equation has the entire expression "3x+4" in the denominator, as opposed to "15/(3x) + 4." This makes a big difference in the solution to the problem, and, for future reference, the correct way to type your problem (assuming I'm reading it correctly) is "9/8 = 15/(3x+4)."

 

Going with "9/8 = 15/(3x+4)," the most common way these proportions are taught is something called cross-multiplication. Cross-multiplication, not to be confused with regular multiplication of fractions, is nothing fancy, just a shortcut for solving a specific type of equation.

 

To perform cross-multiplication, you need to multiply the numerator of the left-hand side by the denominator of the right-hand side. Then, set that product equal to the product of the deonominator of the left-hand side and the numerator of the right-hand side.

 

From there, this problem is a matter of distribution, combining like terms, and solving an equation in a few steps. In my opinion, the trickiest part is handling the order of operations properly.

 

Tip: When doing the cross-multiplication, put the "3x-4" in parentheses. This will give you a visual cue to distribute the 9 to both the 3x and the 4.

 

I hope this helps, and please repost if you have any additional questions or would like a critique of your solution!