Question

Solve the equation. Check for extraneous solutions.

10/x+4=15/4x+4

Answer 1

\[\frac{ 10 }{ x+4 }=\frac{ 15 }{ 4x+4 }\]

Answer 2

\[\frac{10}{x+4}=\frac{15}{4x+4}\iff 10(4x+4)=15(x+4)\] is a start

Answer 3

i would then divide both sides by \(5\) to get
\[2(4x+4)=3(x-4)\] and then multiply out etc

Answer 4

typo there, i meant
\[2(4x+4)=3(x+4)\]

Answer 5

you good from there?

Answer 6

Is the answer an extraneous solution? When I tried plugging in the answer into the original problem, I got a different answers on both sides of the equation.

Answer 7

what did you get for your answer? the one you tried?

Answer 8

to answer your question, no, the solution is not "extraneous" it works

Answer 9

I got x=4/5

Answer 10

me too
lets check it

Answer 11

\[\frac{ 10 }{ x+4 }=\frac{ 15 }{ 4x+4 }\]
\[\frac{ 10 }{ \frac{4}{5}+4 }=\frac{ 15 }{ 4\times \frac{4}{5}+4 }\]

Answer 12

to find the left hand side, multiply top and bottom by \(5\) and get
\[\frac{50}{4+20}=\frac{50}{24}=\frac{25}{12}\]

Answer 13

to find the right hand side, do the same thing
multiply top and bottom by 5 and get
\[\frac{75}{16+20}=\frac{75}{36}=\frac{25}{12}\]

Answer 14

Oh now I get it. I made weird calculations when trying to simplify it and that messed me up. Thank you!!!