Question

Negative four times a number plus nine is no more than the number minus twenty one

Answer 1

4x+9 =< x-21
-4x-x +9 =< x-x-21
-5x +9 =< -21
-5x +9-9 =< -21-9
-5x =< -30
-5x/-5 =< -30/-5 (DANGER divide by neg affects direction of inequality)
x =< 6
CHECK sign
-4x+9 =< x-21
-4*6+9 =< 6-21
-24+9 =<-15
-15 =<-15

-4*7+9 =< 7-21
-28+9 =< 7-21
-19 =< -14 false

-4*5+9 =< 5-21
-20+9 =< -16
-11 =< -16 true

so
x =< 6 is correct.












I use =< since eq would NO MORE THAN.

Answer 2

n is no more than six