Question 109466
a)

{{{abs(x)>-2}}} Start with the given inequality

Since the absolute value of any number is <font size=4><b>always positive</b></font>, this means {{{abs(x)>0}}}. So this means the left side will always be greater than -2. So the solution set is *[Tex \Large \left\{x|x\in\mathbb{R}\right\}]. Basically x can be any number.


b)




{{{abs(x)-2=-3}}} Start with the given equation



{{{abs(x)=-1}}} Add 2 to both sides.



Since the expression {{{abs(x)=-1}}} is <font size=4><b>never</b></font> true (note: remember, the absolute value of any number is <font size=4><b>always positive</b></font>), there are no solutions to {{{abs(x)=-1}}}


Also, notice if we graph {{{y=abs(x)-2}}} and {{{y=-3}}}(just set each side equal to y and graph), we get:


{{{graph(500,500,-10,10,-10,10,abs(x)-2,-3)}}} Graph of {{{y=abs(x)-2}}} (red) and {{{y=-3}}}(green)


and we can see that the two graphs <font size=4><b>never</b></font> intersect. So there are no solutions.