How do I find if the Absolute value of a negative number is no solution or all numbers?

Ok, so I know you can not have an absolute value of a negative number. However, with the equation |2y-9|%26gt;-5 or the equation |x-4|+5%26gt;2 says the solution is all real numbers and the equation |5-4x|%26lt;-6 has no solution. I dont understand how to find if one is no solution or all numbers as I was always told that the absolute value of a negative is always no solution. Can you please help me understand this?How do I find if the Absolute value of a negative number is no solution or all numbers?
|2y-9|%26gt;-5


=%26gt; |2y-9|^2%26gt;(-5)^2


=%26gt; 4y^2 -36y +81 %26gt; 25


=%26gt; 4y^2 -36y +56 %26gt; 0


=%26gt; y^2 -9y +14 %26gt; 0


solve


=%26gt; y^2 -9y +14 = 0


=%26gt; y = 7 OR y = 2


since %26gt; 0


=%26gt; y %26lt; 2 OR y %26gt; 7











QEDHow do I find if the Absolute value of a negative number is no solution or all numbers?
there is no absolute value that is less than a negative number(when it comes to an equation) so thats why in the last equation its no solution, but for example the Absolute value of -5 is 5.