Algebraic Inequalities with Modulus

Question

Can we square both sides in an inequality, if both the equations are inside Modulus, such as below:

|3-X| < |X+4|

What is the algebraic approach to solve these type of questions?

VeritasKarishma  Mam can you please explain

KarishmaB · Answer

Yes, squaring both sides here is the easiest way to deal with them.

subramanya1991 · Answer

VeritasKarishma . Can you pleas explain I d entail the logic behind squaring. And all the scenarios we can use square a mod.

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KarishmaB · Answer

subramanya1991 : When we have an absolute value in our equation or inequality, we try to get rid of the absolute value sign to be able to solve for the variable. Sometimes, we use the definition of absolute values |x| = x if x >= 0 |x| = -x if x < 0 At others we consider absolute value as distance from 0 to logically get the solution. Another method is to square (if we can) because that gets rid of the sign too. |x| > 5 can be squared since both sides are positive. It gives us x < -5 or x > 5 as the solution which is correct. |x| > -5 cannot be squared since one side is positive and other negative (but we know it will hold for all real values of x)

Algebraic Inequalities with Modulus

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