SOLUTION: i would much appreciate help in how to solve this linear equation. without using a graph, how do you find the value of x when the denominator of the fraction is the unknown + a num

Algebra ->  Average -> SOLUTION: i would much appreciate help in how to solve this linear equation. without using a graph, how do you find the value of x when the denominator of the fraction is the unknown + a num      Log On


   

Question 174223: i would much appreciate help in how to solve this linear equation. without using a graph, how do you find the value of x when the denominator of the fraction is the unknown + a numeral.
(6k-3)/(2k+7)=(3k-2)/(k+5)
can you please simplify the answer in a step by step format. Thankyou so much.
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
%286k-3%29%2F%282k%2B7%29=%283k-2%29%2F%28k%2B5%29
First thing to do is clear the denominators. We will need to come back to this step later to verify our 'answer' is a valid one. So cross multiply and clear them.
%286k-3%29%28k%2B5%29=%283k-2%29%282k%2B7%29 Now expand
6k%5E2+%2B30k+-+3k+-+15+=+6k%5E2+%2B+21k+-4k+-14 simplify
6k%5E2+%2B+27k+-+15+=+6k%5E2+%2B+17k+-+14 collect like terms
10k+=+1
k+=+1%2F10
Will that value if k make either of the original denominators = 0? No it won't so, 1/10 is a valid possibility.
Check the original equation using x=(1/10) and verify it satisfies the equation. Does it?
%280.6-3%29%2F%280.2+%2B+7%29+=+%28+0.3-2%29%2F%280.1%2B5%29
%28-2.4%29%2F%287.2%29+=+%28-1.7%29%2F%285.1%29
-1%2F3+=+-1%2F3 which is true. so the answer is 1/10