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# Two Alg 2 Questions-I have answers, I Just Need To Know If I'm Right

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The denominator of a fraction is 2 more than its numerator.

When 1/2 is added to this fraction, the resulting fraction's denominator is twice the denominator of the original fraction and its numerator is 1 more than its denominator.

What is the numerator of the original fraction?

3

5

8

11

What is the exact solution to the equation e^3x+5=9?

x=3/5+ln9

x=3/ln9-5

x=5+ln9/3

x=ln9-5/3

Jan 17, 2018

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The denominator of a fraction is 2 more than its numerator.

When 1/2 is added to this fraction, the resulting fraction's denominator is twice the denominator of the original fraction and its numerator is 1 more than its denominator.

What is the numerator of the original fraction?

We have

x / [ x + 2 ]  +  1/2   =   [ 2 (x + 2)  + 1 ]   / [ 2(x + 2) ]

Simplify

[ 2x +  x + 2 ]  /  [2 (x + 2]  =  [ 2x + 5 ]  / [ 2(x + 2) ]

Multiply through by  2(x + 2)

2x + x + 2    =  2x  + 5

3x  +  2  =  2x  + 5

x  = 3     ⇒  "A"  is correct  !!!!

I think this is.....

e^(3x+5)  = 9         take the  Ln  of both sides

Ln e^(3x + 5)  =  Ln 9

(3x + 5)  Ln e   =  Ln 9    ⇒        { Ln e  = 1}

3x + 5  = Ln 9          subtract 5 from both sides

3x  =  Ln (9)  - 5       divide both sides by 3

x  =   [ Ln (9)   -  5 ]  / 3    ......the last answer is correct....if I've interpreted this correctly

Jan 17, 2018
edited by CPhill  Jan 17, 2018