Question

Solve the following inequality:
$|x-2|⩽|x+4|$

Answer 1

The given equation is

$|x-2|\le |x+4|$

Therefore we have 3 cases

$i.)x\le -4,ii.)-4\le x\le 2,iii.)x\ge 2$

Therefore the respective equations are

$i.)2-x\le -4-x$ which is equal to$2\le -4,$ which is not possible therefore no solution in this case

$ii.)2-x\le x+4$ which is equal to $x\ge -1$

$iii.)x-2\le x+4$ which is equal to $-2\le 4$ which is possible for all values of x and also we assumed $x\ge 2$

Hence the solution is $x\in [-1,\infty )$