Inequalities - question/clarification

GRE Quant Problem Solving
1

Hi,

Basic question just a rule of thumb, how will I know when to “flip the inequality for example. In absolute values there has to be 2 equations for

|x|<=5

plug in -4 for example

|-4|<=5

4 <=5

But in the instance

|2|<=5

Do I just leave as 2<=5 because outside has to be positive?

Do I flip it if it’s something like

|-11|<= 65

Do I flip it to 11>=65

Because outside of that equation to keep the sign the same would be incorrect?

Thank you!

2

just remember these two rules:

  1. | x | ≤ y → -y ≤ x ≤ y
  2. | x | ≥ y → x ≤ -y and x ≥ y

there is no flipping involved in your doubt about.