Question

For the following statements, write True (T) or False (F). If the statement is false, correct the statement.
– 100 is to the right of – 50 on a number line
(a) True
(b) False

Answer 1

Hint: To solve this question, first define and draw the real line on both the positive direction (that is the right-hand side) and the negative direction that is the left-hand side. Then we will study with normal integers on the negative and positive parts and then compare if our statement is true or false.

Complete step by step answer:
The given statement is – 100 is the right of – 50 on a number line. Let us first study the number line to solve this. The real line is one having the values until the negative infinity and till positive infinity as well. It is represented as

The positive real line is the values after 0 on the right-hand side having all the vales of terms as positive. On the right-hand side, we have the positive real axis.
We can say that \[x+1 > x\forall x\in \text{ positive real}\text{.}\] that is, 5 > 4, 6 > 5, 4 > 3, etc.
In the negative real axis, we can see that the numbers are all the same as the right-hand values but they are all negative. Also, the left value is the smallest with respect to the right one.
\[-4<-3\] although \[4>3.\]
Similarly, we have – 3 < – 2 and – 5 < – 4 and so on. So, we get that the value is smaller if it is on the left of some value. That means the number on the right will have a bigger value than their adjacent left ones. For – 5 and – 4, – 5 is left of – 4 and – 4 is right of – 5. – 4 is bigger than – 5.
Now, let us consider our statement. – 100 is to the right of – 50 on a number line. If – 100 is right of – 50, then by the above theory, we have – 100 > – 50. But actually, – 100 < – 50. Therefore, our statement “– 100 is to the right of – 50 on a number line” is false.
The correct statement is “– 100 is to the left of – 50 on a number line”.

So, the correct answer is “Option B”.

Note: Even if we write – 50 is to the right of – 100 on the number line, then that statement is also correct. So, we can also use – 50 is to the right of – 100 on the number line instead of using the statement – 100 is to the left of – 50 on the number line. In the end, both statements are correct.