Question

How would you graph and solve this ?? Plz help! Open to see image.

Answer 1

Check the picture below.

keep in mind that an absolute value expression is in effect a piece-wise.

$\bf |x-4|\le 2\implies \begin{cases} +(x-4)\le 2\\ -------\\ -(x-4)\le 2\\ x-4\ge -2 \end{cases}\implies \begin{array}{llll} -2\le x-4\le 2\\\\ \textit{adding 4 to all 3 sides}\\\\ \boxed{2\le x \le 6} \end{array}\\\\ -------------------------------\\\\ |x-5|\ \textgreater \ 3\implies \begin{cases} +(x-5)\ \textgreater \ 3\\ -------\\ -(x-5)\ \textgreater \ 3\\ x-5\ \textless \ -3 \end{cases}\implies \begin{array}{llll} 3\ \textless \ x-5\ \textless \ -3\\\\ \textit{adding 5 to all 3 sides}\\\\ \boxed{8\ \textless \ x\ \textless \ 2} \end{array}$