Given the function f(x)=-2x+4 what is the real number x such as |x|<-7-f(7).

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

It is given that f(x) = -2x + 4

If |x| < -7 - f(7)

=> |x| < -7 - (-2*7 + 4)

=> |x| < -7 + 2*7 - 4

=> |x| < -7 + 10

=> |x| < 3

=> -3 < x and x < 3

The values of x lie in the interval (-3 , 3)

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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).

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