Equations, inequalities and graphs：練習題

Solve the equation \(|3x + 2| = 8\).

Find the set of values of \(x\) for which \((x + 2)(x - 1)(x - 3) > 0\).

In the diagram, a sketch of the function \(f(x) = (x + 2)(x - 1)(x - 3)\) is shown. Use the sketch to determine the set of values of \(x\) for which \(f(x) > 0\).

Solve the equation \(4|x - 1| = 12\).

Solve the equation \(x - 5\sqrt{x} + 6 = 0\) by using a suitable substitution.

Solve the equation:
\(|3x + 2| = 11\)

Solve the equation \(x^4 - 13x^2 + 36 = 0\) by using an appropriate substitution.

The graph of \(y = |(x-2)(x-4)(x+3)|\) is drawn. State the coordinates of all the points where the graph intersects the x-axis and the y-axis.

Solve the equation \(|2x - 3| = 5\).

Solve the equation \(|x^2 - 6x + 5| = 4\).