SEARCH HOME
 Math Central Quandaries & Queries
 What is the greatest value of 5 – | x – 3 | for any integral value of x. PRANAVM

Hi,

The solution requires that you know the definition of absolute value.

$|z| = \left\{ \begin{array}{rl} z & \mbox{if z \ge 0} \\ -z & \mbox{if z < 0}\end{array}\right.$

Thus for your problem if $|x - 3| \ge 0$, that is if $x \ge 3$ then the expression is

$5 - |x - 3| = 5 - (x - 3) = 5 - x + 3 = 8 - x$

What is the greatest value of $8 - x$ for $x$ an integral and $x \ge 3?$

Now suppose $|x - 3| < 0.$ What does your expression become?

Penny

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.