Sullivan Algebra and Trigonometry: Section 1'1 Linear Equations

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Sullivan Algebra and Trigonometry Section
1.1Linear Equations

• Objectives of this Section
• Solve a Linear Equation
• Solve Equations That Lead to Linear Equations
• Solve Applied Problems Involving Linear Equations

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The set of all values of a variable that make an
equation a true statement are called solutions,
or roots, of the equation.
Example The statement x 5 9 is true when x
4 and false for any other choice of x. Thus, 4
is a solution of the equation. We also say that
4 satisfies the equation x 5 9.

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We solve equations by creating a series of
equivalent equations, that is equations that have
precisely the same solution set.
Example The equations 3x 4 5x and 2x -4
are equivalent equations, since the solution set
for both equation is -2.
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Procedures that Result in Equivalent Equations
1. Interchange the two sides of the equation.
2. Simplify the sides of the equation by
combining like terms, eliminating parenthesis,
and so on.
3. Add or subtract the same expression on both
sides of the equation.
4. Multiply or divide both sides of the equation
by the same nonzero expression.
5. If one side of the equation is 0 and the
other side can be factored, then set each factor
equal to 0.
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Example
Solve
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Example
Solve
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Example
Solve the equation
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A linear equation in one variable is equivalent
to an equation of the form
Note that the previous example,
Is an example of a linear equation, since it is
equivalent to
Both equations have the same solution set

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Example