Sketch y=|linear| and y=linear, solve inequality: numeric coefficients

2

1. Sketch the graph of \(y = | 2 x + 3 |\).
2. Solve the inequality \(3 x + 8 > | 2 x + 3 |\).

2

1. Sketch the graph of \(y = | 2 x - 3 |\).
2. Solve the inequality \(| 2 x - 3 | < 3 x + 2\).

1

1. Sketch the graph of \(y = | 2 x + 1 |\).
2. Solve the inequality \(3 x + 5 < | 2 x + 1 |\).

1

1. Sketch the graph of \(y = | 4 x - 2 |\).
2. Solve the inequality \(1 + 3 x < | 4 x - 2 |\).

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. (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.

4

1. On Figure 1 add a sketch of the graph of $$y = | 3 x - 6 |$$ 4
2. Find the coordinates of the points of intersection of the two graphs.
   Fully justify your answer. \includegraphics[max width=\textwidth, alt={}, center]{b7df05bf-f3fc-4705-a13c-6b562896fa9f-05_2488_1716_219_153}

By sketching the graphs of \(y = |2x + 1|\) and \(y = -x\) on the same axes, show that the equation \(|2x + 1| = -x\) has two roots. Find these roots. [4]