Respuesta :
Answer:
y=-x-4 given that x is less than -2.
Step-by-step explanation:
|x-3|=x-3 when x-3 is positive, [tex]\ge 0[/tex]. So solving [tex]x-3 \ge 0[/tex] by adding 3 on both sides gives [tex]x \ge 3[/tex]
|x-3|=-(x-3) when x-3 is negative, [tex]\le 0[/tex]. So solving [tex]x-3 \le 0[/tex] by adding 3 on both sides gives [tex]x \le 3[/tex]
[tex]x<-2[/tex] is included in the last one since these values are less than 3. This means for our problem with given condition that |x-3|=-(x-3)=-x+3.
|x+2|=x+2 when x+2 is positive, [tex]\ge 0[/tex]. So solving [tex]x+2 \ge 0[/tex] by subtracting 2 on both sides gives [tex]x \ge -2[/tex]
|x+2|=-(x+2) when x+2 is negative, [tex]\le 0[/tex]. So solving [tex]x+2 \le 0[/tex] by subtracting 2 on both sides gives [tex]x \le -2[/tex]
[tex]x<-2[/tex] is included in the last one since these values are less than -2. This means for our problem with given condition that |x+2|=-(x+2)=-x-2.
|x-5|=x-5 when x-5 is positive, [tex]\ge 0[/tex]. So solving [tex]x-5 \ge 0[/tex] by adding 5 on both sides gives [tex]x \ge 5[/tex]
|x-5|=-(x-5) when x-5 is negative, [tex]\le 0[/tex]. So solving [tex]x-5 \le 0[/tex] by adding 5 on both sides gives [tex]x \le 5[/tex]
[tex]x<-2[/tex] is included in the last one since these values are less than 5. This means for our problem with given condition that |x-5|=-(x-5)=-x+5.
Lets put it altogether now.
y=|x−3|+|x+2|−|x−5|, if x<−2
y=-x+3+-x-2-(-x+5)
y=-x+3-x-2+x-5
y=-x-x+x+3-2-5
y=-x-4
