Answer:
1) -4<x<0 = (-4,0)
2) x>=0 = [0, infinity)
3) 0<x<4 = (0,4)
4) -4<x<=4 = (-4,4]
5) x<=0 = (-infinity,0]
Explanation:
Basically, we need to link inequalities with their solutions.
1) -4<x<0: solution to this inequality are all numbers between -4 and 0, or mathematically written (-4,0).
2) x>=0: solution to this are all numbers between 0 (including 0) and positive infinity, or [0, infinity)
3) 0<x<4: all numbers between 0 and 4, or in interval notation (0,4)
4) -4<x<=4: all numbers between -4 and 4 (including 4) which in interval notation is (-4,4]
5) x<=0: all the values from negative infinity to 0 (including 0), which is (- infinity,0]
Note that whenever there is symbol <= or >= we also need to include that value, and for noting that we use square bracket.