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| Algebraic Equations and Inequalities |
 Properties of Equations and Inequalities Graphical Interpretation of Solutions
Linear Equations Linear Inequalities
Linear Equations Involving Absolute Value Linear Equations Involving a Few Absolute Values Linear Inequalities Involving Absolute Value
 Quadratic
EquationsQuadratic Equations and Quadratic Functions Extreme Value of Quadratic Function Quadratic Formula Solving Quadratic Equations by Factoring Quadratic
Inequalities |
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In order to solve an equation involving the absolute value | a x + b |, it is necessary to consider two cases. Case 1. If the expression a x + b represents a positive quantity, then the absolute value symbol can be simply dropped: a x + b ≥ 0 ⇒ | a x + b | = a x + b. Case 2. If the expression a x + b represents a negative quantity, then a x + b < 0 ⇒ | a x + b | = – (a x + b). Thus, to solve a linear equation involving the absolute value | a x + b | means to solve two ordinary linear equations.
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