Question

solve 1+5/x-1>=7/6

Answer 1

Have you tried solving it yet?

Answer 2

\[1+\frac{ 5 }{ x-1 }\ge \frac{ 7 }{ 6 }\]

Answer 3

yes, i got x<=31

Answer 4

What kind of method? You should start also included the methods so it would be easier to solve.

Answer 5

Im sorry, it just says to solve

Answer 6

Just to make yours and my life easier

Answer 7

decompose?

Answer 8

@phi, are you helping him?

Answer 9

\[ 1+\frac{ 5 }{ x-1 }\ge \frac{ 7 }{ 6 } \\
\frac{ 5 }{ x-1 }-\frac{1}{6}\ge 0\\
\frac{31-x}{6(x-1)}\ge 0\\
\frac{31-x}{(x-1)}\ge 0
\]

Answer 10

Yup.

Answer 11

the idea is you want the left-hand side to be positive
that requires both the top and bottom to be positive
or both to be negative.

Answer 12

so 1<x<=31?

Answer 13

close.

Answer 14

yes, it will work out to 1< x <=31

Answer 15

as a quick test, notice x=0 gives a negative number

Answer 16

or why not \[1<x \le 31\]

Answer 17

will you check my answer for this one too?
\[\frac{ 2 }{ x }>\frac{ -1 }{ x-1 }\]

Answer 18

i got x<2/3, x>1

Answer 19

@phi you can have it?

Answer 20

\[ \frac{ 2 }{ x }>\frac{ -1 }{ x-1 } \\
\frac{ 2 }{ x }+\frac{ 1 }{ x-1 } \gt 0 \\
\frac{3x-2}{x(x-1)} \gt 0
\]

Answer 21

test for both top and bottom being positive
3x-2>0
x> 2/3

x(x-1) > 0
this requires x>0 and x>1, which simplifies to x>1
we can rule out x<0 and x<1 (contradicts the top being x>2/3)

so x>1 is required to make top and bottom both positive.

Answer 22

my options are
x>0
x<2/3, x>1
0<x<1
0x<2/3, x>1

Answer 23

test both top and bottom being negative
3x-2<0
x < 2/3

x(x-1)<0
x<0 and x>1 not possible
x> 0 and x<1

0<x<2/3

should also work

Answer 24

yes, the conditions are
0<x<2/3 or x>1

Answer 25

thank you :3