Question

Does anyone know how to solve this inequality? ​

Answer 1

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`(x - 1)/(2) - (x - 2)/(3) > (x - 3)/(4) \\`

Multiply sides by 12

`12 * ( (x - 1)/(2) - (x - 2)/(3) ) > 12 * ( (x - 3)/(4) ) \\`

`(12 * (x - 1)/(2) ) - (12 * (x - 2)/(3) ) > 12 * (x - 3)/(4) \\`

`(6 * \: (x - 1)) - (4 * (x - 2)) > 3 * (x - 3) \\`

`6x - 6 - (4x - 8) > 3x - 9`

`6x - 6 - 4x + 8 > 3x - 9`

`6x - 4x + 8 - 6 > 3x - 9`

Collect like terms

`(6 - 4)x + 2 > 3x - 9`

`2x + 2 > 3x - 9`

`3x - 9 < 2x + 2`

Add sides 9

`3x - 9 + 9 > 2x + 2 + 9`

`3x > 2x + 11`

Subtract sides 2x

`- 2x + 3x > - 2x + 2x + 11`

`x > 11`

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Answer 2

Answer:

(x-1/2)-(x-2/3)>(x-3/4)
Multiply both sides by 12
6(x-1)-4(x-2)>3(x-3)
6x-6-4x+8>3x-9
6x-4x-6+8>3x-9
2x+2>3x-9
Move 3x to the left, and move 2 to the right; change the signs for both
2x-3x>-9-2
-x>-11
Change the signs
x<11