# To Solve Linear Equations

```To Solve Linear Equations
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Clear grouping symbols by using the distribution property
Clear fractions by multiplying the equation by a common denominator
Combine like terms on each side of the equal sign
Isolate the variable
o Use the Addition and Subtraction Properties of Equality
o Use the Multiplication and Division Properties of Equality
o You will have an answer of the form x = 7
o You will have an answer where there is no variable and a FALSE statement …
this is a contradiction (-8 = 7) which in turn means there is no solution (&oslash;)
o You will have an answer where there is no variable and a TRUE statement …
that is an identity (0 = 0) which in turn means the solution set is all Real
Numbers 
Check the solution by using substitution into the ORIGINAL equation
To Solve Rational Expressions
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Find the DOMAIN
Clear grouping symbols by using the distribution property
Clear fractions by multiplying the equation by a common denominator
Combine like terms on each side of the equal sign
Isolate the variable
o Use the Addition and Subtraction Properties of Equality
o Use the Multiplication and Division Properties of Equality
o You will have an answer of the form x = 7
o You will have an answer where there is no variable and a FALSE statement …
this is a contradiction (-8 = 7) which in turn means there is no solution (&oslash;)
o You will have an answer where there is no variable and a TRUE statement …
that is an identity (0 = 0) which in turn means the solution set is all Real
Numbers 
Check the solution
o Is it in the domain?
o Use substitution into the ORIGINAL equation
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Find the DOMAIN
equality
Clear the radical by raising both sides of the equation to the power equal to the index
o Raise sides … NOT terms
o You may need to do this step twice!
Clear grouping symbols by using the distribution property
Clear fractions by multiplying the equation by a common denominator
Combine like terms on each side of the equal sign
Set the equation to ZERO
Solve the resulting quadratic by using
o Factoring
o Completing the Square
o Graphing
o You will have an answer of the form x = 7
o You will have an answer where there is no variable and a FALSE statement …
this is a contradiction (-8 = 7) which in turn means there is no solution (&oslash;)
o You will have an answer where there is no variable and a TRUE statement …
that is an identity (0 = 0) which in turn means the solution set is all Real
Numbers 
Check the solution
o Is it in the domain?
o Use substitution into the ORIGINAL equation
To Solve Absolute Value Expressions
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Isolate the absolute value by using the addition/subtraction/multiplication/division
properties of equality
To solve ax  b  k , solve the compound equation
ax  b  k OR ax  b  k
To solve ax  b  cx  d , solve the compound equation
ax  b  cx  d OR ax  b  (cx  d )
Clear fractions by multiplying the equation by a common denominator
Combine like terms on each side of the equal sign
Isolate the variable
o Use the Addition and Subtraction Properties of Equality
o Use the Multiplication and Division Properties of Equality