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