Question

Which of the following inequations is represented by the the number line below?

• A. $0<6x<36;x\in \text{N}$
• B. $12<6x<36;x\in \text{N}$
• C. $0<5x<25;x\in \text{N}$
• D. $10<5x<30;x\in \text{N}$

Answer 1

The correct option is A $0<6x<36;x\in \text{N}$

We can see solutions on the number line are: 1, 2, 3, 4 and 5.

Let's consider the inequation:
$0<6x<36$

Rule: If both the sides of an inequation are multiplied or divided by the same positive number, then the sign of the inequality will remain the same. Let's apply the above rule in following inequation.
Now, dividing by 6 to both the sides

$\Rightarrow \frac{0}{6}<\frac{6x}{6}<\frac{36}{6}$
$\Rightarrow 0<x<6$
$x=1,2,3,4,5$ {$\therefore x\in \text{N}.$}

Now, let's consider the inequation:

$12<6x<36$
$\Rightarrow \frac{12}{6}<\frac{6x}{6}<\frac{36}{6}$
$\Rightarrow 2<x<6$
$x=2,3,4,5$ {$\therefore x\in \text{N}.$}

Now, let's consider the inequation:

$1<5x<25$
$\Rightarrow \frac{0}{5}<\frac{5x}{5}<\frac{30}{5}$
$\Rightarrow 2<x<6$
$x=1,2,3,4$ {$\therefore x\in \text{N}.$}

Now, let's consider the inequation:
$10<5x<30$
$\Rightarrow \frac{12}{6}<\frac{6x}{6}<\frac{30}{5}$
$\Rightarrow 2<x<6$
$x=2,3,4,5$ {$\therefore x\in \text{N}.$}

So, the inequation that the number line represents is:
​​​​​​​$0<6x<36$