Question

solve for x. (4/6x+3)=(5/5x-8) +1

Answer 1

\[\frac{ 4 }{ 6x+3 }=\frac{ 5 }{ 5x-8 } +\frac{ 5x-8}{ 5x-8 }\]

Answer 2

\[\frac{ 4 }{ 6x+3 }=\frac{ 5x-3 }{ 5x-8 }\]

Answer 3

are the steps making sense so far?

Answer 4

yes they are

Answer 5

\[4(5x-8)=(6x+3)(5x-3)\]

Answer 6

\[20x-32=30x^2-3x-9\]

Answer 7

\[0=30x^2-23x+23\]

Answer 8

Next you use quadratic formula.
\[x=\frac{ -(-23) +or-\sqrt{(-23)^2-4(30)(23)} }{ 2(30)}\]

Answer 9

I really appreciate you taking your time to walk me though the process. thank you so much :)

Answer 10

no problem

Answer 11

\[\frac{ 23+ or -\sqrt{-2231} }{ 60 }\]

Answer 12

so the two possible x values are imaginary.
\[\frac{ 23 }{ 60 } + \frac{ i \sqrt{2231} }{ 60 } and \frac{ 23}{ 60 }-\frac{ i \sqrt{2231} }{ 60 }\]

Answer 13

does the imaginary have a value?

Answer 14

Imaginary numbers do not have values, because they aren't real.

Answer 15

so if i were to check the answer, it wouldn't really check so it would be no solution?

Answer 16

There's a solution, but it's imaginary, so you can't really work with it.

Answer 17

oh okay thank you

Answer 18

No problem, glad to help.