Functions of a Real Variable and Drawing Curves — Solving absolute value equations and inequalities

About this lesson

This unit covers solving absolute value equations and inequalities, both graphically and algebraically. It begins by explaining how to solve equations of the form |ax - b| = c, |ax + b| = cx + d, and |ax + b| = |cx + d|, using graphical methods (plotting the modulus function and a linear or constant function, then finding intersection points) and algebraic methods (using the piecewise definition of the modulus). It also covers properties of absolute value, such as |ab| = |a||b| and |a + b| ≤ |a| + |b|, and includes life applications, like calculating the area of a piece of land between two curves. The unit then moves to solving absolute value inequalities graphically (by comparing curves) and algebraically (using rules like if |x| < a then -a < x < a, and if |x| > a then x > a or x < -a). Exercises are provided for practice. The text also includes an introduction to a separate unit on logarithms, listing objectives and key terms, but the main content of this unit is absolute value equations and inequalities.