I'm stuck with this kind of absolute inequality:
Firstly, when I solve this one:
I make sure the right side of the equation is greater than zero; Condition:
When I solve this by separating it in two cases and finding a solution, I get, in this example: $x=-1.5$, which belongs to the interval of $[-2,+\infty)$, so it's the right solution.
However, when I solve the first inequality $(1)$, I get the solution:
$-1.5$ is in the interval of the condition for the equation $(1)$ (which is the same for the second one -- the inequality): $[-2,+\infty )$, therefore, the WHOLE interval of $(-∞, -1.5)$ is the solution. Is this the right way of solving this kind of inequality?
Thanks in advance.