Tentukan Nilai dari: a. |2x-5| jika x < 0 b. |x-2| jika x < 1 Sederhanakan bentuk berikut: a. |x-1| + |2x-3| jika x < 0 b. |x-4| + |2-x| + |2x-1| jika x > 4 c.

[tex]x<0\rightarrow 2x<0\rightarrow 2x-5<-5<0\rightarrow |2x-5|=-(2x-5)=5-2x[/tex]
[tex]x<1\rightarrow x-2<-1<0\rightarrow |x-2|=-(x-2)=2-x[/tex]

a.
[tex]x<0\rightarrow x-1<-1<0\rightarrow |x-1|=-(x-1)=1-x[/tex]
[tex]x<0\rightarrow 2x<0\rightarrow 2x-3<-3<0\rightarrow |2x-3|=-(2x-3)=3-2x[/tex]
[tex]\therefore |x-1|+|2x-3|=1-x+3-2x=4-3x[/tex]

b.
[tex]x>4\rightarrow x-4>0\rightarrow |x-4|=x-4[/tex]
[tex]x>4\rightarrow -x<-4\rightarrow 2-x<-2<0\rightarrow |2-x|=-(2-x)=x-2[/tex]
[tex]x>4\rightarrow 2x>8\rightarrow 2x-1>7>0\rightarrow |2x-1|=2x-1[/tex]
[tex]\therefore |x-4|+|2-x|+|2x-1|=x-4+x-2+2x-1=4x-7[/tex]

c.
[tex]x<0\rightarrow 2x-1<0\rightarrow |2x-1|=-(2x-1)=1-2x[/tex]
[tex]x<0\rightarrow x-3<0\rightarrow |x-3|=-(x-3)=3-x[/tex]
[tex]x<0\rightarrow 1-x>0\rightarrow |1-x|=1-x[/tex]
[tex]\therefore |2x-1|+|x-3|+|1-x|=1-2x+3-x+1-x=5-4x[/tex]