Question

Please please please I need help with this question!

Solve 1+5/x-1>/7/6

or

1 plus 5 over x-1 is greater than or equal to 7 over 6

Answer 1

\[\frac{1+5}{x-1}\geq \frac{7}{6}\] like that?

Answer 2

or maybe
\[\large 1+\frac{5}{x-1}\geq \frac{7}{6}\] would make more sense

Answer 3

Yes like that!

Answer 4

ok you need first to subtract \(\frac{7}{6}\) from both sides to get
\[\frac{5}{x-1}-\frac{1}{6}\geq 0\]

Answer 5

then you have to actually subtract and write as one fraction
\[\frac{30-(x-1)}{6(x-1)}\geq 0\] or
\[\frac{31-x}{6x-6}\geq 0\]

Answer 6

the denominator is \(0\) if \(x=1\) and the numerator is \(0\) if \(x=31\) so this will change sign at \(1\) and \(31\)
you want to know where it is \(\geq 0\) i.e. positive, so one way to find out is to test a number
i pick \(0\) and \(\frac{31}{-6}<0\) so it is negative on \((-\infty,1)\) then positive on \((1,31)\) and then negative on \((31,\infty)\)

Answer 7

your "final answer" is
\[(1,31]\] or
\[1<x\leq 31\]

Answer 8

THANK YOU SO MUCH!!!!!!!!!!!!!!!!!!!!!!