Question

State true or false \[\left| { - 4} \right| - 4 = 8\]
A). True
B). False

Answer 1

Hint: In the given question, we have been given to solve an expression containing the modulo function. We must know what this thing does – if the expression is positive, it does not do anything, but if the expression is negative, it adds another negative sign, so as to make the expression positive. In other words, the modulo expression gives the absolute value of any numeral.

Formula used:
We are going to use the modulus property:
\[\left| n \right| = \left| { - n} \right| = n\]

Complete step by step solution:
We have to check if the following given expression is true or false:
\[\left| { - 4} \right| - 4 = 8\]
If the left-hand side and the right-hand side are equal, then the statement is true, else false.
First, let us solve the left-hand side:
now to solve this side, we are going to use the modulus property:
\[\left| n \right| = \left| { - n} \right| = n\]
So, \[\left| { - 4} \right| = 4 \Rightarrow \left| { - 4} \right| - 4 = 4 - 4 = 0\]
We have \[LHS = 0\] and \[RHS = 8\]
Hence, \[LHS \ne RHS\]
Thus, the correct option is B – false.

Note: In the given question, we had to write if the given statement was true or false. We did that by solving the two sides of the expression. For that, we solved the modulus function. We must know what that function is without which we cannot know or solve any question containing it. So, we just need to remember the basics of the function – it converts any expression (positive or negative) to positive.