Algebra 2-

Question

If one is added to the reciprocal of three times a number, the result is five times the reciprocal of the number.  What is the number?

Answer 1

1+(1/3x)=5/x this means that:

 

(3x+1)/3x=5/x if we cancel the x it gives us the following equation:

 

3x+1=15 

 

x=14/3

 

Regards,

Answer 2

n represents the number

3n represents three times the number

1/3n represents the reciprocal of three times the number

1/n represents the reciprocal of the number

 

1 + 1/3n = 5(1/n)   

3n + 1 = 15             multiply both side by LCD, 3n

3n = 14                    subtract 1 from both sides

n = 14/3                  divide both sides by 3

 

Check:

3n = 14

1 + 1/14 = 5(3/14)

15/14 = 15/14

 

Answer 3

First set up the equation 1+1/3x=5(1/x) now simplify and solve. we can change the 1 into 3x/3x which gives us (3x+1)/(3x)=(5/x) continuing (3x+1)=(15x/x) which can be rewritten as 3x+1=15 subtracting the one gives us 3x=14 so x is 14/3 which is 2.666666666666 repeating or about about 2.67.