The diagram shows the graph of \(y=|3x+3|\).

Use a graphical method to solve the inequality \(|3x+3|\geqslant |x-2|\).

Solve the following inequalities.

(a) \(x^2-x-6\geqslant0\)

(b) \(|3x-4|\lt x+2\)

Solve the inequality \(|5 x+2| \geqslant 3\).

(a) On the axes, sketch the graphs of \(y=4|x-1|\) and \(y=|3x+2|\), stating the intercepts with the axes.

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

Use a graphical method to solve the inequality \(|2 x-8|\gt 4\).

(a) Solve the equation \(2|8-4 x|+5=25\).

(b) Solve the inequality \(16 x-5 x^{2}-3\lt \frac{57-9 x}{6}\).

(a)

Draw the graphs of \(y=|2 x-5|\) and \(y=|4-x|\) for \(-2 \leqslant x \leqslant 6\).

(b) Use your graphs to solve the inequality \(|4-x| \leqslant|2 x-5|\).

(a) Solve

\(\frac{|4x-5|}{7}=1.\)

(b) The diagram shows the graph of \(y=|3x+9|\). By drawing a suitable graph on the same diagram, solve

\(|3x+9|\leq |x-5|.\)

(a) On the axes, sketch the graphs of \(y=2x+5\) and \(y=|4x-3|\), stating the intercepts with the coordinate axes.

(b) Solve the inequality \(|4x-3| \lt 2x+5\).

Solve the inequality

\(\left|5x+4\right|\lt \left|2x-3\right|.\)

The graph of \(y=|4-3x|\) is sketched on the axes.

(a) State the coordinates of the points where the graph cuts the coordinate axes.

(b) Solve the inequality

\(|4-3x|\geq 7.\)

(a) Solve the inequality

\(|4x-1|\gt 9.\)

(b) Solve the equation

\(2x-11\sqrt{x}+12=0.\)

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