Solve |linear| compared to linear

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

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

4

1. Sketch, on the same diagram, the graphs of \(y = | 3 - x |\) and \(y = 9 - 2 x\).
2. Solve the inequality \(| 3 - x | > 9 - 2 x\).
3. Use logarithms to solve the inequality \(2 ^ { 3 x - 10 } < 500\). Give your answer in the form \(x < a\), where the value of \(a\) is given correct to 3 significant figures.
4. List the integers that satisfy both of the inequalities \(| 3 - x | > 9 - 2 x\) and \(2 ^ { 3 x - 10 } < 500\).

2 Solve the inequality \(| x - 7 | > 4 x + 3\).

2 Solve the inequality \(| x - 7 | > 4 x + 3\).

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

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

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

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

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

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

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

5. (a) Sketch the graph with equation $$y = | 4 x - 3 |$$ stating the coordinates of any points where the graph cuts or meets the axes. Find the complete set of values of \(x\) for which
(b) $$| 4 x - 3 | > 2 - 2 x$$ (c) $$| 4 x - 3 | > \frac { 3 } { 2 } - 2 x$$

1. Find the set of values for which

$$| x - 1 | > 6 x - 1$$

1. (a) Sketch the graph with equation

$$y = | 2 x - 5 |$$ stating the coordinates of any points where the graph cuts or meets the coordinate axes.
(b) Find the values of \(x\) which satisfy $$| 2 x - 5 | > 7$$ (c) Find the values of \(x\) which satisfy $$| 2 x - 5 | > x - \frac { 5 } { 2 }$$ Write your answer in set notation.

1. Find the set of values for which

$$| x - 1 | > 6 x - 1$$ [P4 January 2002 Qn 2]

1

1. If \(| x | = 3\), find the possible values of \(| 2 x - 1 |\).
2. Find the set of values of \(x\) for which \(| 2 x - 1 | > x + 1\). Give your answer in set notation.