Question

Write the absolute value of $x-6,$.if $x$ is greater than $6$.

Answer 1

Absolute value:

Absolute value means the magnitude of a real number without regard to its sign whether it is positive or negative.

In mathematics, it is defined as $\left|x\right|=\left\{\begin{array}{l}-x,ifx<0\\ x,ifx\ge 0\end{array}\right.$.

Since,

$$\begin{gathered} x>6\Rightarrow x-6>0; \\ \Rightarrow x-6ispositive \end{gathered}$$

Therefore, $|x-6|=x-6$

Hence, $\left|x-6\right|=x-6,x\ge 6$.