Question

Solve the following inequality:
$x^2-7x+12<|x-4|$

Answer 1

$x^2-7x+12<|x-4|$

$(x-3)(x-4)<|x-4|$

Squarring both sides.

$(x-4{)}^2(x-3{)}^2<(x-4{)}^2$

$(x-4{)}^2(x^2-6x+9-1)<0$

$(x-4{)}^2(x-2\left)\right(x-4)<0$

$(x-4{)}^3(x-2)<0$

$xϵ(2,4)$