Question 1140329
<br>
{{{abs(A) = A}}} if A >= 0;
{{{abs(A) = -A}}} if A < 0.<br>
(1) If x < -2.5, then...<br>
2x+5 and 2x-5 are both <0, so<br>
{{{abs(2x+5) = -(2x+5)}}}
{{{-abs(2x+5) = 2x+5}}}
{{{abs(2x-5) = -(2x-5) = -2x+5}}}
{{{-abs(2x+5)+abs(2x-5) = (2x+5)+(-2x+5) = 10}}}<br>
(2) If x >= 2.5, then...<br>
2x+5 and 2x-5 are both >0, so<br>
{{{abs(2x+5) = 2x+5}}}
{{{-abs(2x+5) = -(2x+5) = -2x-5}}}
{{{abs(2x-5) = 2x-5}}}
{{{-abs(2x+5)+abs(2x-5) = (-2x-5)+(2x-5) = -10}}}<br>
(3) If -2.5 < x <= 2.5, then...<br>
2x+5 >0 and 2x-5 < 0, so<br>
{{{abs(2x+5) = 2x+5}}}
{{{-abs(2x+5) = -(2x+5) = -2x-5}}}
{{{abs(2x-5) = -(2x-5) = -2x+5)}}}
{{{-abs(2x+5)+abs(2x-5) = (-2x-5)+(-2x+5) = -4x}}}<br>
Summary:<br>
y = 10; if x < -2.5
y = -4x; if -2.5 <= x <= 2.5
y = -10; if x > 2.5<br>
A graph....<br>
{{{graph(400,400,-5,5,-15,15,-abs(2x+5)+abs(2x-5))}}}<br>