Question

Solve the inequality, 3x – 5 < x + 7, when

(i) x is a natural number

(ii) x is a whole number

(iii) x is an integer 

(iv) x is a real number

Answer 1

We have 3x – 5 < x + 7

⇒ 3x < x + 12  (Adding 5 to both sides)

⇒ 2x < 12 (Subtracting x from both sides)

⇒ x < 6 (Dividing by 2 on both sides)

(i) Solution set is {1, 2, 3, 4, 5}

(ii) Solution set is {0, 1, 2, 3, 4, 5}

(iii) Solution set is {....– 3, – 2, –1, 0, 1, 2, 3, 4, 5}

(iv) Solution set is {x : x ∈ R and x < 6}, i.e., any real number less than 6.