Question

Write the absolute value of $x-8,ifxisgreaterthan8.$.

Answer 1

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,

$$\begin{gathered} x>8,impliesx-8>0; \\ i.e,x-8ispositive. \\ Therefore,\left|x-8\right|=x-8. \end{gathered}$$