please help 10 points?

4x-10>=14 ,,,add 10 to both sides
4x-10+10>=14+10
4x>=24 ,,,devide by 4,,,,x>=24/4=6
[ 6,infinity)
abs(2x+15)>17
2x+15>17 or 2x+15<-17
2x>17-15 or 2x ,-17-15
2x>2 or 2x<-32
x>2/2 or x<-32/2
x>1 or x<-16
(-infinity,-16) u (1,infinity)

1.
4x ≥ 24
x ≥ 6
sol. set is { x : x ≥ 6 }

2.
2x + 5 > 17 ___or ____2x + 5 < - 17
2x > 12______ or_____2x < -22
x > 6 ________or_____x < -11

Well,
4x – 10 ≥ 14
is equivalent to
4x – 10 + 10 ≥ 14 + 10
4x + 0 ≥ 24
1/4 * 4 * x ≥ 24/4
1 * x ≥ 6
x ≥ 6
therefore, the set S of solutions is :
S = [6, +oo)

|2x + 5| > 17
is equivalent to
2 * |x + 5/2| > 17
|x + 5/2| > 17/2
|x - (-5/2) | > 17/2
in other words, the distance from x to (-5/2) is greater than 17/2
-5/2 + 17/2 = 6
and
-5/2 - 17/2 = -11
therefore, the set S of solutions is :
S = (-oo, -11) U (6, +oo)

qed
et voilà, mademoiselle !! ;-)

hope it' ll help !!