Solve each of the following in equations and represent the solution set on the number line.

5x + 2 < 17, where (i) x ϵ Z, (ii) x ϵ R.

(i) 5x + 2 < 17, x є Z

Subtracting 2 from both the sides in the above equation,

5x + 2 – 2 < 17 – 2

5x < 15

Dividing both the sides by 5 in the above equation,

x < 3

Since x is an integer

Therefore, possible values of x can be

x = {…, -2, -1, 0, 1, 2}

(ii) 5x + 2 < 17, x є R

Subtracting 2 from both the sides in above equation

5x + 2 – 2 < 17 – 2

5x < 15

Dividing both the sides by 5 in above equation

x < 3

Therefore, x є (-∞, 3)