Given the function f(x)=-2x+4 what is the real number x such as |x|

By definition, we'll
have:

|x|<-7-f(7) <=> -[-7-f(7)]
< x < -7-f(7)

7+f(7) < x <
-7-f(7)

We'll solve the left side
inequality:

7+f(7) <
x

We'll replace f(7) by f(7) = -2*7 + 4 =
-10

7 - 10 < x

-3
< x

We'll solve the right side
inequality:

x <
-7-f(7)

x < -7 -
(-10)

x < -7 + 10

x
< 3

The real values of x, that
accomplish the constraint |x|<-7-f(7), are located in the opened interval (-3 ,
3).