Question

when you add the same number to both sides of an inequality , does the inequality remain true

Answer 1

Yes, The Reason Why, Is If You Add The Same To Both Sides, It Still Remains True. For Example:
10*5+2 < 10*6
But, If You Add 6 To Both Sides:
10*5+8< 10*6+6.
It Is The Same As
50+8<60+6.
In Conclusion, This Means That As Long As You Add The Same Number To Both Sides, Not Just One, But Both Sides, Your Inequality Will Always Stay The Same! (Unless You Change Something That You Aren't Supposed To Like Making Is (10+6)*5+2 < 6*10+6)

Answer 2

It would be the same, because the number is the same, so an example:
4*3 and 5*3, it would be 12 and 15, but if you add 5 to each side, then it would be, 4*3+5 and 5*3+5, then you would get 17 and 20. So to answer the question, yes the inequality would remain true because the number that you are adding to each side is the same. It is the same with dividing and multiplying and subtracting.