Question

On a number line, numbers on the left side are ________ numbers on the right side.
(a) Greater than
(b) Smaller than
(c) Equal to
(d) None of the above

Answer 1

Hint: For knowing the answer we need to consider the number line of some range and then we need to compare the numbers on the left side and right side assuming any number as an index. In general, we consider ‘0’ as an index and consider numbers on the left and right side of ‘0’ and then compare all the numbers.

Complete step-by-step solution
Let us assume the number line of the range of (-5,5) as follows

Let us assume that ‘0’ is the index value.
By comparing the number ‘1’ with all the values on left side of ‘0’ we get
\[\begin{align}
  & 1>-1 \\
 & 1>-2 \\
 & 1>-3 \\
\end{align}\]
Here, we can conclude that ‘1’ is greater than all the values on left side of ‘0’
Now, let us compare the number ‘2’ with all values on left side of ‘0’ we get
\[\begin{align}
  & 2>-1 \\
 & 2>-2 \\
 & 2>-3 \\
\end{align}\]
Here, we can conclude that ‘2’ is greater than all the values on left side of ‘0’
Now, let us compare the number ‘3’ with all values on left side of ‘0’ we get
\[\begin{align}
  & 3>-1 \\
 & 3>-2 \\
 & 3>-3 \\
\end{align}\]
Here, we can conclude that ‘3’ is greater than all the values on left side of ‘0’
Now, let us compare the number ‘4’ with all values on left side of ‘0’ we get
\[\begin{align}
  & 4>-1 \\
 & 4>-2 \\
 & 4>-3 \\
\end{align}\]
Here, we can conclude that ‘4’ is greater than all the values on left side of ‘0’
Now, let us compare the number ‘5’ with all values on left side of ‘0’ we get
\[\begin{align}
  & 5>-1 \\
 & 5>-2 \\
 & 5>-3 \\
\end{align}\]
Here, we can conclude that ‘5’ is greater than all the values on left side of ‘0’
Similarly, we can conclude this for all the numbers.
Therefore, we can say that numbers on the left side are less than numbers on the right side of a number line. So, option (b) is the correct answer.

Note: We can also solve the problem in an indifferent way. We know that in a number line if we consider ‘0’ as an index then, on the left side of ‘0’ there will be negative numbers and on the right side of ‘0’ there will be positive numbers. Also, we know that negative numbers are always less than positive numbers. So, we can conclude that the left side numbers are always less than the right side numbers.