Question

x minus 1 divided by x minus 3 is less than 1

Answer 1

$\frac { x - 1 }{ x - 3 } < 1$

Subtracting 1 from both sides. we get,

$\frac{x - 1 }{ x - 3 } - 1 < 1 - 1$

=> $\frac{x -1 }{x - 3 } - 1 < 0$

Taking LCM and solving we get,

=> $\frac{ x - 1 }{ x - 3 } - \frac{ (x - 3 ) }{ x - 3 } < 0$

=> $\frac{ x - 1 - x + 3 }{ x - 3 } < 0$

=> $\frac{ 2 }{x - 3 } < 0$

x cannot be 3. This is because if x = 3 then the denominator will become 3 -3 and the fraction will 2 / 0 which is in-determinant or undefined. Hence x must be less than 3 to satisfy the condition x < 0.

So x = ( -∞ , 3 )

Hope it helped !