Question

Fill in the blanks with correct inequality sign (>, <, ≥, ≤).

(i) x > –3 ⇒ –2x ………. 6 

(ii) a < b and c > 0 ⇒ \(\frac{a}{c}\) ……….\(\frac{b}{c}\)

(iii) p – q = –3 ⇒ p ………. q 

(iv) u – v = 2 ⇒ u ………. V

Answer 1

(i) x > -3 ⇒ -2x ……… 6 

As, x > -3 

Multiplying both sides by 2

Then, 

2x > -6 

Now multiplying both the sides by -1 

2x(-1) < 6(-1) 

-2x > 6 

Therefore, 

x > -3 ⇒ -2x > 6

(ii) a < b and c > 0 \(\Rightarrow \frac{a}{c} ............ \frac{b}{c}\)

As, a < b …(1) 

c > 0 

Dividing both sides by c in equation (1) 

Then,

\(\frac{a}{c} < \frac{b}{c}\)

Therefore, 

a < b and c > 0 \(\Rightarrow\)\(\frac{a}{c} < \frac{b}{c}\)

(iii) p – q = -3 ⇒ p ……… q 

As, 

p – q = -3 

p = q - 3 

From the above equation it is clear that p would always be less than q 

Therefore

p – q = -3 ⇒ p < q 

(iv) u – v = 2 ⇒ u ……… v 

As, u – v = 2 u = v + 2 

From the above equation it is clear that u would always be greater than v 

Therefore, 

u – v = 2 ⇒ u > v