Question 1 Report
(a) If \(9 \cos x - 7 = 1\) and \(0° \leq x \leq 90°\), find x.
(b) Given that x is an integer, find the three greatest values of x which satisfy the inequality \(7x < 2x - 13\).
(a) \(9\cos x-7=1\Rightarrow 9\cos x=8\Rightarrow \cos x=\dfrac{8}{9}=0.8889\).
For \(0^{\circ}\le x\le 90^{\circ}\): \(x=\cos^{-1}(0.8889)\approx \mathbf{27.3^{\circ}}\).
(b) \(7x<2x-13 \Rightarrow 7x-2x<-13 \Rightarrow 5x<-13 \Rightarrow x<-2.6\).
Since \(x\) is an integer, the values are \(\ldots,-5,-4,-3\). The three greatest are \(\mathbf{-3,\ -4,\ -5}\).
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