2 < | x + 5 | < 3 | 1 − x | 2 < | x + 5 | a n d | x + 5 | < 3 | 1 − x | {\displaystyle {\begin{aligned}&2<|x+5|<3|1-x|\\&2<|x+5|and|x+5|<3|1-x|\\\end{aligned}}}
2 < | x + 5 | x + 5 > 2 ; X + 5 < − 2 {\displaystyle {\begin{aligned}&2<|x+5|\\&x+5>2&;X+5<-2\\\end{aligned}}}
X + 5 < − 2 X < − 7 {\displaystyle {\begin{aligned}&X+5<-2\\&X<-7\\\end{aligned}}}
לאחר השוואת הבסיסים לאפס, הצבת המספרים על ציר המספרים, התחומים הם :
x = − 6 | − 6 + 5 | − 3 | 1 − ∗ − 6 | < 0 ( − ) ( + ) < 0 ↓ − ( x + 5 ) − 3 ( 1 − x ) < 0 {\displaystyle {\begin{aligned}&x=-6\\&|-6+5|-3|1-*-6|<0\\&(-)(+)<0\\&\downarrow \\&-(x+5)-3(1-x)<0\\\end{aligned}}}
X = 0 | 0 + 5 | − 3 | 1 − 0 | < 0 ( + ) ( + ) < 0 ↓ ( x + 5 ) − 3 ( 1 − x ) < 0 {\displaystyle {\begin{aligned}&X=0\\&|0+5|-3|1-0|<0\\&(+)(+)<0\\&\downarrow \\&(x+5)-3(1-x)<0\\\end{aligned}}}
x = 3 | 3 + 5 | − 3 | 1 − 3 | < 0 ( + ) ( − ) < 0 ↓ ( x + 5 ) + 3 ( 1 − x ) < 0 {\displaystyle {\begin{aligned}&x=3\\&|3+5|-3|1-3|<0\\&(+)(-)<0\\&\downarrow \\&(x+5)+3(1-x)<0\\\end{aligned}}}
− ( x + 5 ) − 3 ( 1 − x ) < 0 − x − 5 − 3 + 3 x < 0 2 x − 8 < 0 2 x < 8 x < 4 {\displaystyle {\begin{aligned}&-(x+5)-3(1-x)<0\\&-x-5-3+3x<0\\&2x-8<0\\&2x<8\\&x<4\\\end{aligned}}}
( x + 5 ) − 3 ( 1 − x ) < 0 x + 5 − 3 + 3 x < 0 4 x + 2 < 0 4 x < 2 x < 1 2 {\displaystyle {\begin{aligned}&(x+5)-3(1-x)<0\\&x+5-3+3x<0\\&4x+2<0\\&4x<2\\&x<{\frac {1}{2}}\\\end{aligned}}}
( x + 5 ) + 3 ( 1 − x ) < 0 x + 5 + 3 − 3 x < 0 − 2 x + 8 < 0 − 2 x < 8 x > 4 {\displaystyle {\begin{aligned}&(x+5)+3(1-x)<0\\&x+5+3-3x<0\\&-2x+8<0\\&-2x<8\\&x>4\\\end{aligned}}}
2 < | x + 5 | {\displaystyle \ 2<|x+5|} וגם | x + 5 | − 3 | 1 − x | < 0 {\displaystyle \ |x+5|-3|1-x|<0}
x ≤ 1 2 ; x > 4 {\displaystyle x\leq {\frac {1}{2}};x>4}
X < 7 − 3 < x ≤ 1 2 X > 4 {\displaystyle {\begin{aligned}&X<7\\&-3<x\leq {\frac {1}{2}}\\&X>4\\\end{aligned}}}
