kkrrsshh wrote:

I have read all the above explanations, but I still dont understand how can an absolute/modulus of any term equals its negative value. Imho |x|=x and |-x|=x. Could you please throw some light on this? May be I am interpreting it wrong.

I solved the statement 1 using test values viz. x=-4,-5,-6 .

Hi

kkrrsshh,

Definition of modulus:

For any real number \(x\), modulus is defiend as follows:

\(|x| = \begin{cases} x, & \mbox{if } x \ge 0 \\ -x, & \mbox{if } x < 0. \end{cases}\)

To solve any modulus question first find the critical point(i.e. a value or point where sign changes).

In case of |x+4| critical point is -4. So we have following:

\(|x+4| = \begin{cases} x+4, & \mbox{if } x \ge -4 \\ -(x+4), & \mbox{if } x < -4. \end{cases}\)

Now you can check whether above expression satisfies the modulus property or not.

Consider x = -5 , in this case |x+4| = -(x+4) = -(-5+4) = 1 (a positive value)

x = -2 , in this case |x+4| = x+4 = -2+4 = 2 (again a positive value)

x = -4, |x+4| = x+4 = -4+4 = 0 (a non-negative value).

Hope it helps.