# State whether true or false.The absolute value of an integer is greater than the integer.A. TRUEB. FALSE (2023)

Hint: Here we use the definition of absolute value of an integer and using the definition we compare both the values in magnitude. Absolute value is the modulus of a number.

We know the set of integers contains all the negative numbers, zero and all the positive numbers and can be written as the set $Z = \{ .... - 3, - 2, - 1,0,1,2,3....\}$
So, if we look at a real line, integers are extended on both sides.
Now we know that the absolute value of an integer is defined as the numeric value of the integer without considering the sign along with it. Absolute value of an integer $x$ is denoted by a modulus sign $\left| x \right|$.
Value of $\left| x \right| = x$ if $x$ is positive.
Value of $\left| x \right| = - x$ if $x$ is negative.
Absolute value of an integer is always non-negative as the negative sign along with the integer gets removed when we apply modulus to it.
So, the absolute values of integers are represented on a real line from zero to infinity, which means the whole real line except the negative numbers.
If we take an integer $- x$, then absolute value of the integer will be $\left| { - x} \right| = - ( - x) = x$ which is positive. So, we can say the absolute value of an integer is greater than the integer.
If we take an integer $x$, then absolute value of the integer will be $\left| x \right| = x$ which is positive. So, we can say the absolute value of an integer is equal to the integer.
From both the above statements we conclude that the absolute value of an integer is greater than or equal to the value of the integer.
So, the statement given in the question is wrong.
So, option B is correct.

Note: Students many times make mistake while calculating the absolute value of a negative integer as they take only the numeric value in place of $x$ in $\left| x \right| = - x$ where they have to take the negative sign along with the numeric value then only the both negative signs will multiply to give positive value.

## FAQs

### Is the absolute value of an integer greater than the integer? ›

The absolute value of an integer is always greater than the corresponding integer.

Is the absolute value of a number greater than the number? ›

The absolute value of a real number x is denoted by |x| and is defined as |x|={xif x≥0−xif x<0. Therefore, the absolute value is always greater than or equal to zero, and describes how far away the corresponding number is from the origin. The absolute value of a real number is sometimes referred to as its modulus.

Is the absolute value of an integer always less than the integer True or false? ›

The absolute value of an integer is always greater than the integer. No worries!

What is true about the absolute value of an integer? ›

The absolute value of a number or integer is the actual distance of the integer from zero, in a number line. Therefore, the absolute value is always a positive value and not a negative number.

Is the absolute value of an integer less than the integer? ›

Absolute value of an integer is always non-negative as the negative sign along with the integer gets removed when we apply modulus to it. So, the absolute values of integers are represented on a real line from zero to infinity, which means the whole real line except the negative numbers.

Is the absolute value of an integer equal to the opposite of the integer? ›

In general, any positive integer and its opposite will have the same absolute value. To find the opposite of an integer, just change its sign either from positive to negative or from negative to positive.

Is the absolute value of an integer greater than zero? ›

The absolute value of an integer is greater than zero. This statement is FALSE because zero is an integer as well, therefore getting the absolute value of zero will result to zero.

Can an absolute value be greater than a negative number? ›

If the absolute value part is greater than a negative value, then you have "all real solutions," because any x value will keep the absolute value positive, and that will always be greater than a negative value.

Is the absolute value of a number always greater than its opposite? ›

A number and the opposite of the number always have the same absolute value.

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