Guided Practice Write a compound inequality that represents the situation.

all real numbers that are between –4 and 6

A.
–4 < x and x > 6, or –4 < x > 6

B.
–4 > x and x > 6, or 6 < x < –4

C.
–4 < x and x < 6, or –4 < x < 6

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)