1) the solution to the inequality
10x + 18 < −2 is A. x<−2
proof: 10x + 18 < −2 and 10x < −2 -18=-20 so 10x<-20 implies x< -20/10=-2
2) the solution to the inequality
−6x + 5 > −1 is B. x<1
proof: −6x + 5 > −1 -6x>-1-5= -6, - 6x> -6 implies x< -6/-6=1
3) let's solve −4.2y + 2.1 > −2.52
if −4.2y + 2.1 > −2.52 so −4.2y > −2.52 - 2.1= - 4.62
−4.2y > - 4.62 implies y< - 4.62 / - 4.2=1.1
so y<1.1
4) let's solve −4/3x + 1/6 < 7/9
if −4/3x + 1/6 < 7/9 then −4/3x < 7/9 -1/6=7/9 -1/6 (multiplied by 3 for each member) we have −4x < 7/3 -1/2=(2x7-1x3)/2x3=11/6, it means −4x < 11/6
and then x>11/-24, x> -11/24
the solution set of
−9.5x−1.5>−30 can be found by solving this inequation,
−9.5x>−30 +1.5 −9.5x> -28.5 so it means x< 28.5/9.5=3
x<3, the solution set is S= ] -infinity, 3[
