Inequality concept problem

Question

Hello I am a student and had the following problems in inequality: $-2\le 1 $ Squaring both sides the sign changes $4\gt 1$ But for $-1\lt 1$ Squaring the terms we get $1\le 1$ I am stuck here please help me to understand this concept

Answer 1

You have committed a serious error. In inequalities like $a<b$, you can only multiply both sides by the same number, and you cannot square both sides. In addition, you have to change the multiplication sign if you multiply a negative number. T square both sides, it only holds for inequalities like $|a|<|b|$.

Answer 2

The inequality signs don't remain the same if one of the sides is negative. But the inequality sign can remain the same even after squaring if the absolute value i.e. the magnitude of the numbers on either side of inequality sign follows the sign of inequality.

I hope this clarifies your doubts.