3. Equations, inequalities and graphs

• solve graphically or algebraically equations of the type |ax + b| = c (c ⩾ 0) and |ax + b| = |cx + d|
• solve graphically or algebraically inequalities of the type |ax + b| > c (c ⩾ 0), |ax + b| ⩽ c (c > 0) and |ax + b| ⩽ |cx + d|
• use substitution to form and solve a quadratic equation in order to solve a related equation
• sketch the graphs of cubic polynomials and their moduli, when given in factorised form y = k(x – a)(x – b)(x – c)
• solve cubic inequalities in the form k(x – a)(x – b)(x – c) ⩽ d graphically