Why No Solution For Inequality Equation?

[SCSmith]

|2-5x|> -8

I am thinking an absolute value can't have a negative number. Let's see...

2-5x< -(-8)
-5x<6 subtract 2 from both sides
x< -6/5 divide by -5

or


2-5x>8
-5x>6 subtract 2 from both sides
x>-6/5

So x is all real numbers less and greater than -6/5

My question is (if that above answer is right), is how can you tell if an inequality equation has no solution. Do you have to work out the equation in each case or can you tell just by inspection of the original problem?

 

[pka]

There is absolutely nothing to do here!
For every x, |x|>-8.
So the solution set for the given problem is the set of all real numbers.