Solve 5x-3 < 7, when (i) x is an integer(ii) x is a real number

Let's solve the inequality 5x - 3 < 7 step by step for both cases:

Step 1: Solve the inequality for x.
We are given: 5x - 3 < 7

First, isolate the term with x. Add 3 to both sides of the inequality: 5x - 3 + 3 < 7 + 3

Simplifying this: 5x < 10

Now, divide both sides of the inequality by 5: x < 10 / 5

Simplifying this: x < 2

(i) When x is an integer:
For x to be an integer, x can take any integer value less than 2. Therefore, the integer solutions are: x = -1, 0, 1

(ii) When x is a real number:
For x to be a real number, x can take any real value less than 2. So, the solution is: x < 2 (where x is any real number less than 2)

Final Answers:
(i) If x is an integer, the solution is: x = -1, 0, 1

(ii) If x is a real number, the solution is: x < 2