Question

Which of the following inequalities, where x is an integer, is/are satisfied by the solution set $x=3,4,5$?
(I) $3x>9$
(II) $x-1\ge 2$
(III) $x+3>5$

• A. II only
• B. I and II only
• C. II and III only
• D. I, II and III

Answer 1

The correct option is C II and III only

(i)$3x>9$

Divided both sides by 3 we get

$3x÷>9÷3$

$\Rightarrow x>3$

The value of $x$ greater than $3$ is $4,5,6,........$

The solution set is not satisfied.

(ii) $x-1\ge 2$

Add 1 both sides we get

$x-1+1\ge 2+1$

$\Rightarrow x\ge 3$

The value of $x$ greater than and equal to $3$ is $3,4,5,6,.........$

The solution set is satisfied.

(iii) $x+3>5$

Add $-3$ both sides we get

$x+3-3>5-3$

$\Rightarrow x>2$

The value of $x$ greater than $2$ is $3,4,5,6,.........$

The solution set is satisfied.

Then II and III satisfy solution set.