# Equations and inequalities

The topic is divided into the following subtopics:
• Linear equations and inequalities
• Higher degree equations and inequalities
• Rational equations and inequalities
• Absolute value equations and inequalities
• Equations and inequalities with parameters
• Systems of linear equations and inequalities
• Systems of nonlinear equations and inequalities

### Linear equations and inequalities

Part I:
• Simple linear equations
• Equivalent equations
• Graphical solutions of linear equations
• Linear equations specified by word description
Part II:
• Simple linear inequalities
• Graphical solutions of linear inequalities
• Linear inequalities specified by word description
Part III:
• Word problems leading to linear equations and inequalities

Part I:
Part II:
• Vieta’s formulas
Part III:
• Quadratic equations and inequalities with absolute value
• Word problems – more complex

### Higher degree equations and inequalities

Part I:
• Equations solvable by factoring polynomials to products of linear and quadratic factors
Part II:
• Equations solvable by substitution method
• Cubic equations with one of the roots known
• Inequalities solvable by factoring polynomials to products of linear and quadratic factors
Part III:
• Equations of 4th degree with two of the roots known
• Equations of higher degrees, guessing of some of the roots is necessary

### Rational equations and inequalities

Part I:
• Rational equations
• Domains of rational equations
Part II:
• Rational inequalities
• Domains of rational inequalities
Part III:
• Rational equations and inequalities with absolute values

### Absolute value equations and inequalities

Part I:
• Linear equations and inequalities with single absolute value - solutions based on geometric interpretation of the absolute value
Part II:
• Linear equations with one or more absolute values
Part III:
• Linear inequalities with one or more absolute values
• Linear equations and inequalities with absolute values inserted in absolute values

Part I:
• Equations with an unknown under a single radical
• Domain of an equation
• Domain of an expression with an unknown under a radical
Part II:
• Equations with unknown under several radicals
• Inequalities with unknowns under radicals
Part III:
• Word problems
• More complex equations – combinations of radicals and absolute values

### Equations and inequalities with parameters

Part I:
• Linear equations with a parameter
• Equations and inequalities with a parameter solved for a given value of the parameter
Part II:
• Linear inequalities with a parameter
• Quadratic equations and inequalities with a parameter
Part III:
• Rational equations and inequalities with a parameter

### Systems of linear equations and inequalities

Part I:
• Systems of two equations with two unknowns
• One equation with two unknowns
Part II:
• Systems of three equations with three unknowns
• Using matrices to solve systems of equations
• Solvability of systems of equations
• Cramer's rule
• Word problems
• Systems of equations with parameters
Part III:
• Systems of inequalities
• One inequality with two unknowns
• Two inequalities with one unknown

### Systems of nonlinear equations and inequalities

Part I:
• Systems with linear and quadratic equations
• One nonlinear equation with two unknowns
• Systems with an unknown in the denominator
Part II:
• Systems of polynomial equations
• Graphical solutions of systems of polynomial equations
Part III:
• Systems with the unknown in absolute value
• Systems with the unknown under the square root
• Systems with parameter
• Systems of inequalities