Paper 1 · inequalities / indices

Solve the inequality $|3^{-3x} - 54| < 27$ .

-\tfrac{4}{3} < x < -1

1 < x < \tfrac{4}{3}

-\tfrac{4}{3} < x < \tfrac{4}{3}

x < -\tfrac{4}{3}

x > -1

Explanation:

|3^{-3x}-54|<27

gives

27<3^{-3x}<81

, i.e.

3^3<3^{-3x}<3^4

, so

3<-3x<4

and hence

-\tfrac{4}{3}<x<-1

Derived from ZIMSEC Mathematics Paper 1, June 2011, Q1

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