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Equations and Inequalities
Barnett, Ziegler, and Byleen, chapter 2
Mathematical expressions...are no longer just the
mutterings of bearded thinkers who cannot remember to
wear socks of the same color. ...mathematical
expressions give us a way of thinking about relationships
that would otherwise be unavailable to us.
What awaits you in college-level mathematics is an
excitement that is inseparable from hard work.
Sheila Tobias, Succeed with Math
sections:
2-1, 2-2, 2-3, 2-4, 2-5, 2-6, 2-7
The primary focus is to manipulate equations and inequalities to solve these for the unknown. This
chapter continues the review of elementary algebra with a discussion of equations. However, it moves
through linear inequalities and quadratic equations including complex numbers.
objectives:
- tell what is meant by a solution set
- distinguish between an identity and a conditional equation
- use the rules for changing an equation
- identify a linear equation
- solve a linear equation by manipulating the equation
- apply linear equations to a variety of real problems
- explain what is a system of linear equations
- solve a system of two simultaneous linear equations by substitution
- set up a system of equations for application problems
- distinguish between equalities and inequalities
- describe a solution set in terms of the interval notation
- graph the solution set on a number line
- describe the difference between the solution set for an equality and an inequality
- tell how the rules differ for equalities and inequalities
- solve linear inequalities using the rules for manipulating an inequality
- solve double linear inequalities
- define an absolute value
- evaluate an absolute value
- tell how the solution set differs for a linear equation that involves an absolute value
- solve linear equations that involve absolute values
- solve linear inequalities that involve absolute value
- identify a quadratic equation
- explain why the set of real numbers must be extended in order for quadratic equations
- use the imaginary unit, i, to name a complex number
- compute powers of i
- add, subtract, and multiply two complex numbers using i
- compute the conjugate of a complex number
- multiply a complex number by its conjugate
- perform division of a complex number by a complex number and reduce to standard form
- compute the square root of a negative real number, expressing the result as an imaginary
- express a quadratic equation in standard form
- solve a quadratic equation when b = 0
- solve a quadratic equation when c = 0
- solve a quadratic equation by factoring
- solve a quadratic equation by completing the square
- solve a quadratic equation by using the quadratic formula
- write out the quadratic formula
- compute the discriminant and tell the nature of the solution set
- identify equations that might be reducible to quadratic form
- solve equations that involve a radical
- determine any restricted values and eliminate them from the solution set
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© 1999, 2000, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008 by Lawrence Turner |