MHB Inequality solve (x+1)/6<x-(3x-2)/4

[karush]

View attachment 9261
Ok a student sent this to me yesterday so want to answer without too many steps

I think the first thing to do is multiply every
term by 12

$2(x+1)<12x-3(3x-2)$
Expanding
$2x+2<12x-9x+6$

 

[skeeter]

That’s fine.

 

[karush]

That’s fine.

$\dfrac{x+1}{6}<x-\dfrac{3x-2}{4}$
Expanding
$2x+2<12x-9x+6$
Combine like terms
$2x+2<3x+6$
Subtract 2x from both sides
$2<x+6$
Subtract 6 from both sides
$-4<x$

Hopefully no typos

Looks like answer a.