Solve |linear| < constant

1 Solve the inequality \(| 2 x - 7 | > 3\).

1 Solve the inequality \(| 2 x - 3 | > 5\).

1 Find the set of values of \(x\) satisfying the inequality \(| 8 - 3 x | < 2\).

1 Solve the inequality \(| 3 x + 1 | > 8\).

1 Solve the inequality \(| 4 - 5 x | < 3\).

1. (i) Solve the inequality

$$| x - 0.2 | < 0.03$$ (ii) Hence, find all integers \(n\) such that $$\left| 0.95 ^ { n } - 0.2 \right| < 0.03$$

1 Solve the inequality \(| 2 x - 1 | \leqslant 3\).

2

1. Sketch the graph of \(y = | 2 x - 3 |\).
2. Hence, or otherwise, solve the inequality \(| 2 x - 3 | < 5\). Illustrate your answer on your graph.

4 Solve the inequality \(| 2 x + 1 | \geqslant 4\).

7 Solve the inequality \(| x - 1 | < 3\).

9 Solve the inequality \(| 2 x - 1 | \leqslant 3\).

3

1. Sk tcht b g a \(\phi \quad y = | 2 x - 3 |\).
2. Sb the in a \(\operatorname { litg } x \rightarrow \quad | 2 x - 3 |\).

1 Solve the inequality \(| x - 1 | < 3\).

2 Solve the inequality \(| 2 x + 1 | \geqslant 4\).

2 Solve the inequality \(| 2 x + 1 | > 4\).

3 Solve the inequality \(| 2 x - 1 | \geq 4\).

2 Solve the inequality \(| 2 x + 1 | < 5\).

2 The straight line \(y = 5 - 2 x\) is shown in the diagram. \includegraphics[max width=\textwidth, alt={}, center]{20639e13-01cc-4d96-b694-fb3cf1828f4d-04_705_773_881_239}

1. On the copy of the diagram in the Printed Answer Booklet, sketch the graph of \(y = | 5 - 2 x |\).
2. Solve the inequality \(| 5 - 2 x | < 3\).

2 The graph of \(y = | 1 - x | - 2\) is shown in Fig. 2. \begin{figure}[h] \end{figure} Determine the set of values of \(x\) for which \(| 1 - x | > 2\).

13

1. Find \(\mathrm { f } ( x )\) [0pt] [2 marks]
   13
2. Sketch the graph of the function. \includegraphics[max width=\textwidth, alt={}, center]{1d017497-11b1-4096-b83a-63314188307e-14_867_1054_1795_493} 13
3. Find the range of values of \(x\) for which \(\mathrm { f } ( x ) \leq 5\)

4

1. Sketch the graph of \includegraphics[max width=\textwidth, alt={}, center]{08e1f291-7052-40a5-b7b2-13fd1d0137c2-04_933_1093_349_475} 4
2. Solve the inequality $$4 - | 2 x - 6 | > 2$$

7 The function f is defined by $$f ( x ) = \left| \sin x + \frac { 1 } { 2 } \right| \quad ( 0 \leq x \leq 2 \pi )$$ Find the set of values of \(x\) for which $$f ( x ) \geq \frac { 1 } { 2 }$$ Give your answer in set notation.