Solve |linear| > |linear|

1 Solve the inequality \(| 5 x + 7 | > | 2 x - 3 |\). \includegraphics[max width=\textwidth, alt={}, center]{76df3465-9617-4f2b-a8b7-f474b2817504-02_67_1653_333_244} \includegraphics[max width=\textwidth, alt={}, center]{76df3465-9617-4f2b-a8b7-f474b2817504-02_2715_37_143_2010}

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

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

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

2 Solve the inequality \(| x - 8 | > | 2 x - 4 |\).

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

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

1 Solve the inequality \(| 4 x + 3 | > | x |\).

1 Given that \(a\) is a positive constant, solve the inequality $$| x - 3 a | > | x - a |$$

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

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

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

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

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

1 Solve the inequality \(| x + 2 | > \left| \frac { 1 } { 2 } x - 2 \right|\).

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

1. Find the set of values of \(x\) such that

$$| 2 x - 3 | > | x + 2 |$$

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

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

5

1. Give full details of a sequence of two transformations needed to transform the graph of \(y = | x |\) to the graph of \(y = | 2 ( x + 3 ) |\).
2. Solve the inequality \(| x | > | 2 ( x + 3 ) |\), showing all your working.

Solve the inequality \(|x - 3| > 2|x + 1|\). [4]