Question

How much less than $-2$ is $-6$ ?

Answer 1

Hint: Here in the given question we need to find the value of -2 less than -6. The given numbers are negative integers, to solve the problem we need to know the properties of integers. Here on rewriting the numbers in equation form using the transposing process we will get to know the solution.

Complete step by step answer:
Integers are collections of positive and negative numbers along with zero. Set of integers is represented with the letter ‘$Z$’. Unlike whole numbers and natural numbers, integers contain negative numbers. Thus the properties of integers slightly differ from usual addition and subtraction of numbers when it includes negative numbers.

Let the unknown in the problem be assumed as $x$, on framing the given information into the equation form we get,
\[ - 2 - x = - 6\] ---------- (1)
Now this is in the linear equation form we know to solve the unknown using the rules of linear equation. We can now transpose $-2$ on to the left hand side and $-x$ on to the right side thus the sign changes respectively.
\[ - x = - 6 + 2\]

Here using the basic rules of arithmetic operations for integers, we know that when one integer is positive and the other is negative we take the difference of the absolute value of the numbers and then assign the greater number sign among both integers,
\[ - x = - 4\]
On cancelling the signs on both the sides
\[\therefore x = 4\]

Thus the number less than -2 to get -6 is 4.

Note:Here absolute value means the sign of any given number is always considered to be positive. Thus always the absolute value of integers is a positive number. Knowing absolute value plays an important role in the solving integers, prominently while adding and subtracting the integers