Question

Решите неравенства
|2x+1|<3
|3x-2|>7
|4x+3|≥5
|1-2x|≤5

Answer 1

$|2x+1|<3\\\\\left \{ {{2x+1<3} \atop {2x+1<-3}} \right. \\\\\left \{ {{2x<3-1} \atop {2x<-3-1}} \right. \\\\\left \{ {{2x<2} \atop {2x<-4}} \right. \\\\\left \{ {{x<2:2} \atop {x<-4:2}} \right. \\\\\left \{ {{x<1} \atop {x<-2}} \right.$

x ∈ ( -∞ ; -2 )

$|3x-2|>7\\\\\left \{ {{3x-2>7} \atop {3x-2>-7}} \right. \\\\\left \{ {{3x>7+2} \atop {3x>-7+2}} \right. \\\\\left \{ {{3x>9} \atop {3x>-5}} \right. \\\\\left \{ {{x>9:3} \atop {x>-5:3}} \right. \\\\\left \{ {{x>3} \atop {x>-1\frac{2}{3} }} \right.$

x ∈ ( 3 ; +∞ )

$|4x+3|\geq 5\\\\\left \{ {{4x+3\geq 5} \atop {4x+3\geq -5}} \right. \\\\\left \{ {{4x\geq 5-3} \atop {4x\geq -5-3}} \right. \\\\\left \{ {{4x\geq 2} \atop {4x\geq -8}} \right. \\\\\left \{ {{x\geq 2:4} \atop {x\geq -8:4}} \right. \\\\\left \{ {{x\geq 0,5} \atop {x\geq -2}} \right.$

x ∈ [ 0,5 ; +∞ )

$|1-2x|\leq 5\\\\\left \{ {{1-2x\leq 5} \atop {1-2x\leq -5}} \right. \\\\\left \{ {{-2x\leq 5-1} \atop {-2x\leq -5-1}} \right. \\\\\left \{ {{-2x\leq 4} \atop {-2x\leq -6}} \right. \\\\\left \{ {{x\geq 4:-2} \atop {x\geq -6:(-2)}} \right. \\\\\left \{ {{x\geq -2} \atop {x\geq 3}} \right.$

x ∈ [ 3 ; +∞ )