Question

\(\dfrac{x-3}{2}\) - \(\dfrac{4x-1}{3}\) < \(\dfrac{2x-5}{4}\)

Answer 1

\(\Leftrightarrow\dfrac{6\left(x-2\right)-4\left(4x-4\right)-3\left(2x-5\right)}{12}< 0\)

\(\Leftrightarrow6x-12-16x+16-6x+15< 0\)

\(\Leftrightarrow-16x+19< 0\)

\(\Leftrightarrow-16x< -19\)

\(\Leftrightarrow x>\dfrac{19}{16}\)

Answer 2

    `[ x - 3 ] / 2 - [ 4x - 1 ] / 3 < [ 2x - 5 ] / 4`

`<=>[ 6 ( x - 3 ) ] / 12 - [ 4 ( 4x - 1 ) ] / 12 < [ 3 ( 2x - 5 ) ] / 12`

`<=> 6x - 18 - 16x + 4 < 6x - 15`

`<=> 6x - 16x - 6x < -15 + 18 - 4`

`<=>-16x < -1`

`<=> x > 1 / 16`

Vậy `S = { 1 / 16 }`