Question

Solve
2 – x/4≤1 + x/3; 3 – x < 4(x – 3), when (i) x is an integer (ii) x is a real

Answer 1

Answer:

The given inequality is 3x+8>2

⇒3x+8−8>2−8

⇒3x>−6

⇒

3

3x

>

3

−6

⇒x>−2

(i) The integers greater than −2 are −1,0,1,2,.......

Thus when x is an integer, the solutions of the given inequality are −1,0,1,2............

(ii) When x is a real number, the solutions of the given inequality are all the real numbers, which are greater than −2.

Thus in this case, the solution set is (−2,∞)