SOLUTION: These are extra problems I need help to understand to bring up my grade please help I don't get it Find the value for the given variable Show all steps and check answers showing a

Algebra ->  Expressions-with-variables -> SOLUTION: These are extra problems I need help to understand to bring up my grade please help I don't get it Find the value for the given variable Show all steps and check answers showing a      Log On


   

Question 210664: These are extra problems I need help to understand to bring up my grade please help I don't get it
Find the value for the given variable Show all steps and check answers showing all work. Not sure how to type in the problem.
a+1/6 = 2/a or a+1 over 6 = 2 over a
and
5/3x+1 = 3/3x-1 or 5 over 3x+1 = 3 over 3x-1










Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
%28a%2B1%29%2F6+=+2%2Fa+ multiply both sides by a to clear the denominator on the right
a%2A%28a%2B1%29%2F6+=+2 multiply both sides by 6 to clear the denominator on the left
a%2A%28a%2B1%29+=+12 expand the left side
a%5E2+%2B+a+=+12 subtract 12 from both sides
a%5E2+%2B+a+-+12+=+0 factor or use the quadratic equation. Here is a good URL to help check your factoring -->http://72.3.253.76:8080/webMathematica3/quickmath/page.jsp?s1=algebra&s2=factor&s3=basic
%28a%2B4%29%28a-3%29+=+0 in order for a product to be 0, one or more terms in the product must be 0. So in our case, either a%2B4+=0 or a-3=0
So solving those two equations, says either a=-4 or a=3 are solutions to the problem.
Substitute those values for a into the original equation to check your answers.

2)Use the same steps as above.
5%2F%283x%2B1%29+=+3%2F%283x-1%29 Clear right side denominator
%285%2A%283x-1%29%29%2F%283x%2B1%29+=+3 Clear left side denominator
5%2A%283x-1%29+=+3%2A%283x%2B1%29 this time, expand both sides
15x+-5+=+9x+%2B+3 collect like terms
15x+-+9x+=+3+%2B+5 simplfy
6x+=+8 divide both sides by 6
+x+=+8%2F6
x+=+4%2F3 simplify
Here is a great website for math. You can use it to verify your work. For this problem the URL is --> http://www.wolframalpha.com/input/?i=5%2F(3x%2B1)+%3D+3%2F(3x-1)