Question

The sum of two successive integer is greater than 18. Find the smallest number which can satisfy.

• A. 8
• B. 9
• C. 10
• D. 11

Answer 1

The correct option is B 9

Let the first integer be $=x$
The second succcessive integer is $=x+1$
Given, The sum of two successive integer is greater than 18.
This can be written in a mathemtical equation as:
$\Rightarrow x+(x+1)>18$

Add the variables,
$\Rightarrow 2x+1>18$

Subtract 1 from both sides of the inequality
$\Rightarrow 2x>18-1$
$\Rightarrow 2x>17$

Divide by 2 on both sides of the inequlity:
$\Rightarrow \frac{2x}{2}>\frac{17}{2}$
$\Rightarrow x>\frac{17}{2}$
$\Rightarrow x>8.5$

As $x$ is an integer and $x$ is greater than 8.5 :
Values of $x$: 9, 10, 11, 12....
It can be represented on the number line as:
A opened circle at $8.5$ and the red line goes to the right, indicating that $x$ is greater than $\mathrm{8.5.}$


The smallest number $=x=9$
Then, the sum of two succcessive integer $=x+1=9+1=10$