Step 1. Solve both inequalities for

:




Step 2. To check a point in the solution of the given system of inequalities, look for the intercepts of the lines

and

:

(1)

(2)
Replace (1) in (2):

Solve for

:


(3)
Replace (3) in (1):



We can conclude that the point (-2,3) is in the solution of the system if <span>
inequalities</span>
; also any point inside the dark shaded area of the graph of the system of inequalities is also a solution of the system.
To answer this, you just go around multiplying the terms from the first set by everything in the second set. (For example, multiply 2x^2 by x^2, next by -2x, and finally by 5)
X+24*(1/x)=11
x+24/x=11
x²+24=11x
x²-11x+24=0
(x+3)(x-8)=0
x=-3, x=8
checking : 8+24*(1/8)=11, 8+3=11 correct
-3+24*(1/-3)=-3-8=-11 incorrect
number is 8, reciprocal is 1/8