(A Level) The modulus function

Learning objectives

Explain |x| as the non-negative size of x, and rewrite statements such as |x − a| < b as the double inequality a − b < x < a + b

Sketch graphs of y = |ax + b| and y = |ax + b| + c, showing the vertex and the points where the graph meets the axes

Solve equations such as |3x − 2| = |x + 4| or |2x + 1| = 5 − x, either by squaring both sides or by considering separate cases, and check every root

Solve inequalities such as |x − 3| > 2|x + 1| using |a| < |b| ⇔ a² < b², or by reading the solution set from a sketch of both graphs