Question

Solve the following inequality:
$|x-4|<x-1$

Answer 1

The given equation is:

$|x-4|<x-1$ there are 2 possible cases $i.)x<4,ii.)x>4$

and the respective equations in 2 cases are

$i.)4-x<x-1,ii.)x-4<x-1$

$1^{s}t$ case:

$i.)2x>5$ implies $x>\frac{5}{2}$ and we assumed $x<4$

therefore the solution is $\frac{5}{2}<x<4$

$2^{n}d$ case

$ii.)-4<-1$ which is possible for all values of x and we assumed $x>4$

therefore the solution is $x\in (\frac{5}{2},\infty )$