The quotient of 9 and a number is less than the sum of the number and 21.

Answer 1

9/x < x+21, multiply by x

9< x^2 + 21, subtract 9

0< x^2 +21x -9, complete the square

9+ (21/2)^2 < x^2 +21 + (21/)^2

9+441/4 < (x+21/2)^2

477/4 < (x+21/2)^2

(+1/2)sqr477< x+21/2

x>0.42 and x<-21.42

x is an element of the two intervals (-infinity,-21.42) U (0.42,+infinity)

Unless, by chance, you really intended to ask x/9 < x + 21. Then

x<9x + 189

-189<8x

8x>-189

x > -189/8

x > -23.625

but when you say quotient of two numbers, the first number of the two is the dividend, and the 2nd is the divisor