Question

the sum of anumber x and twice another is 20.if the product of these numbers is not more than 48 , whate are all possible values of x?

Answer 1

one number ---- x
the other number --- y

x + 2y = 20
x = 20-2y or y = (20-x)/2

xy ≤ 48
(20-2y)(y) ≤ 48

-2y^2 + 20y - 48 ≤ 0
y^2 - 10y + 24 ≥ 0
(y-6)(y-4) ≥ 0
y ≤ 4 OR y ≥ 6

(20-x)/2 ≤ 4 OR (20-x)/2 ≥ 6
20-x ≤ 8 OR 20-x ≥ 12
-x ≤ -12 OR -x ≥ -8

x ≥ 12 OR x ≤ 8

Answer 2

{X:xless than or equal to 8}U{x: x is geater than or equal to 12}

Answer 3

very good

Answer 4

(x)(y) ≤ 48 And x+2y=20
(20-2y)(y) ≤ 48 x=20-2y or y=(20-x)/2 choose one of the two
20y-2y^2 ≤ 48 (20-x)/2 ≥ 6 or (20-x)/2 ≤ 4
-2y^2+20y-48 ≥ 0 20-x ≥ 12 20-x ≤ 8
y^2-10y+48 ≥ 0 -x ≥ 12-20 -x ≤ 8-20
y^2-6y-4y+48 ≥ 0 x ≤ 8 x ≥ 12
y(y-6)-4(y-6) ≥ 0
(y-6)(y-4) ≥ 0 S,S = {x : x ≤ 8}U{x : x ≥ 12}
y ≥ 6 and y ≤ 4 THANK YOU!!!!