Sketch two |linear| functions and solve related equation/inequality

Sketch two modulus of linear functions on the same diagram (e.g. y=|3x+2a| and y=|3x-4a|), find intersection points and axis intercepts, and solve related equation or inequality. No pre-drawn graph provided.

4 questions · Moderate -0.6

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CAIE P2 2020 June Q4

7 marks Moderate -0.3

Sketch, on the same diagram, the graphs of $y = | 3 x + 2 a |$ and $y = | 3 x - 4 a |$, where $a$ is a positive constant. Give the coordinates of the points where each graph meets the axes.
Find the coordinates of the point of intersection of the two graphs.
Deduce the solution of the inequality $| 3 x + 2 a | < | 3 x - 4 a |$.

CAIE P2 2020 Specimen Q3

6 marks Moderate -0.8

3 It is given that $a$ is a positive constant.

1. Sketch on a single diagram the graphs of $y = | 2 x - 3 a |$ and $y = | 2 x + 4 a |$.
2. State the coordinates of each of the points where each graph meets an axis.
Solve the inequality $| 2 x - 3 a | < | 2 x + 4 a |$.

AQA C3 2006 June Q4

8 marks Moderate -0.8

Sketch and label on the same set of axes the graphs of:
1. $y = | x |$;
2. $y = | 2 x - 4 |$.
1. Solve the equation $| x | = | 2 x - 4 |$.
2. Hence, or otherwise, solve the inequality $| x | > | 2 x - 4 |$.

WJEC Unit 3 2023 June Q7

10 marks Moderate -0.3

The graphs of $y = 5x - 3$ and $y = 2x + 3$ intersect at the point A. Show that the coordinates of A are $(2, 7)$. [2]
On the same set of axes, sketch the graphs of $y = |5x - 3|$ and $y = |2x + 3|$, clearly indicating the coordinates of the points of intersection of the two graphs and the points where the graphs touch the $x$-axis. [4]
Calculate the area of the region satisfying the inequalities $$y \geqslant |5x - 3| \quad \text{and} \quad y \leqslant |2x + 3|.$$ [4]