Question

9|r-2|-10<-73

r<-5
r<9

Answer 1

When I type it into a calculator online it says it is no solution but I am confused on why that is

First thing I did was add 10 to the other side so I got -63

Then I did 9|r-2|<-63 or 9|r-2|<63
Next I divide 9 and got -7 on one and 7 on the other and then added 2 so I got -5 and 9.

Answer 2

9|r-2|-10<-73
9|r-2| < -63
|r - 2| < -7

BUT, the absolute value of anything has to be ≥ 0, so it certainly cannot be ≤ -7

Your inequation has no solution.

Just try some numbers in your solution, they don't work.
e.g. for r < 9 , let r = 4
LS = 9|4-2) - 10 = 8
RS = -73
is 8 < -73 ?? , not when I went to school.