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statement in which two expressions, at least one containing the variable, are set equal.
Equation in one variable
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the expressions in an equation in one variable
sides of the equation.
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the admissible values of the variable, if any, that result in a true statement are called?
solutions. Or Roots
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means to find all the solutions of the equation
solve an equation
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The following equations are all equations in one variable, x:
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we say this because a true statememt results.
4 "____" the equation x+5=9, because, when 4 is substituted for x, a true statememt results.
satisfies
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Sometimes an equation will have more than one solution -2 and 2, Usually, we write the solutions of an equation as a set, called the "_______ ___" of the equation.
Solution set.
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equations having the same solution set.
equivalent equations.
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Procedures that result in equivalent equations.
Interchange the two sides of the equation.
3=x
x=3
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Procedures that result in equivalent equations.
Simplify the sides of the equation by combining like terms, eliminating parentheses, and so on:
(x+2)+6=2x+(x+1)
x+8=3x+1
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Procedures that result in equivalent equations
Add or subtract the same expression on both sides of the equation:
3x-5=4
(3x-5)+5=4+5
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Procedures that result in equivalent equations
Multiply or divide both sides of the equation by the same nonzero expression:
 x≠1
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Procedures that result in equivalent equations
If one side of the equation is 0 and the other side can be factored, then write it as the product of factors:
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Warning
Squaring both sides of an equation does not necessarily lead to an equivalent equation. For example,x=3 has one solution, but x^2 =9 has two solutions, -3 and 3
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Steps for solving Equations:
Step 1
List any restrictions on the domain of the variable.
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Steps for Solving Equations
Step 2:
Simplify the equation by replacing the original equation by a succession of equivalent equations using the procedures listed earlier.
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Steps for Solving Equations
Step 3:
If the result of step 2 is a product of factors equal to 0 use the Zero-Product Property to set each factor equal to 0 and solve the resulting equations.
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Steps for Solving Equations
Step 4
Check your Solutions
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