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## Solving Linear EQUATIONS

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**WHAT IS AN EQUATION?**• A mathematical statement that two expressions is equivalent • Solution set of an equation is the value or values of the variable that make the equation true**General form**• Linear equation in one variable- general form is ax=b where a and b are constants • a is not equal to zero. • Examples: • 4x=8 • 3x-5=2**Linear equation variables**• The variable has no exponents, is not under a radical sign, and is not in the denominator of a fraction.**Solving linear equations**• Goal is to move everything with the variable to one side of the equation • Move everything without a variable to the other side of the equal sign • Must use properties of equality**Solving linear equations**• Isolate the variable • Perform the inverse, or opposite of every operation in the equation • What you do to one side you must do to the other • Inverse operations are done in the reverse order of PEMDAS • Add, subtract first, then divide or multiply to isolate the variable**Solve**• 3(2-3p)=42**solve**• -3(5-4r)=-9**Solve**• 3(w+7)-5w=w+12**solve**• 5(x-6)=3x-18+2x**solve**• 3(2-3x)=-7x-2(x-3)**inequalities**• A statement that compares two expressions by using the <,> symbols. • The graph of an inequality is the solution set (the set of all points on the number line that satisfy the inequality) • Properties of Equality discussed earlier apply to inequalities**The inequality difference**• If you multiply or divide both sides by a negative number, you must reverse the inequality symbol**solve**• Solve and graph on an number line • 9x=4<12x-11**solve**• x+8