Question

dau coroana vă rog este la matematică algebră..este ex.16​

Answer 1

a) |x-3|<4

-4<x-3<4

-4<x-3

x-3>-4

x>-4+3

x>-1=> x€(-1,infinit)

x-3<4

x<7 => x€(-infinit,7)

=>x€(-infinit,7)intersectat(-1,infinit)

=>x€(-1,7)intersectat cu Z

=>x€{0,1,2,3,4,5,6}

b)|-2x+1|<=5

-5<=-2x+1<=5

-5<=-2x+1

-2x+1>=-5

-2x>=-6

-x>=-3 |*(-1)

x<=3 (cand inmultim cu (-1) se schimba semnul !!!)

=>x€(-infinit,3]

-2x+1<=5

-2x<=4 |*(-1)

2x>=-4

x>=-2 => x€[-2,infinit)

=> x€[-2,infinit)intersectat(-infinit,3]

x€{-2,-1,0,1,2,3}

c) |2-3x|<=4

-4<=2-3x<=4

-4<=2-3x

2-3x>=-4

-3x>=-6

-x>=-2 |*(-1)

x<=2 => x€(-infinit,2]

2-3x<=4

-3x<=2 | *(-1)

3x>=-2

x>=-2/3

x€[-2/3,infinit)

=>x€(-infinit,2]intersectat[-2/3,infinit)

-2/3=-0,6

x€{0,1,2}