Question

For what integer value of x is 3x+5>11 and x-3 <1?

Answer 1

3x + 5 > 11
3x + (5 - 5) > 11 - 5 
3x > 6
3x / 3 > 6 / 3
x > 2

x - 3 < 1
x (-3 + 3) < 1 + 3
x < 4

When subtracting / adding values to both sides, the inequality does not change.

When multiplying / dividing by a positive value, the inequality also doesn't change, but when multiplying , dividing with a negative value, the inequality must be flipped.