SOLVING EQUATIONS 8 EE 7 Objective To create

SOLVING EQUATIONS 8. EE. 7

Objective: To create a foldable for the 6 steps to solving equations

Solving Equations Foldable SOLVING EQUATIONS & SYSTEMS Look for the DISTRIBUTIVE PROPERTY (distribute if necessary) Look to COMBINE LIKE TERMS on the same side of the Equation Move the Variable Terms to the same side (use opposites) Undo the WEAK LINKS ADDITION/SUBTRACTION (use opposites) Undo the STRONG LINKS MULTIPLICATION/DIVISION (multiply by reciprocal) Verify (CHECK) (use substitution & order of operations) SPECIAL CASES LINEAR SYSTEMS

STEPS REASON Given Distributive Property Look for the DISTRIBUTIVE PROPERTY

STEPS REASON Given Distributive Property Combine Like Terms Look to COMBINE LIKE TERMS on the same side

STEPS REASON Given Distributive Property Combine Like Terms Addition Axiom of Equality Inverse Property of Addition / Combine Like Terms Move the Variable Terms to the same side (use opposites)

STEPS REASON Given Distributive Property Combine Like Terms Addition Axiom of Equality Inverse Property of Addition / Combine Like Terms Undo the WEAK LINKS ADDITION/SUBTRACTION (use opposites) [CONSTANTS]

Given Distributive Property Combine Like Terms Addition Axiom of Equality Inverse Property of Addition / Combine Like Terms Multiplication Axiom of Equality Inverse Property Simplify of Multiplication / Undo the STRONG LINKS MULTIPLICATION/DIVISION (multiply by reciprocal) [COEFFICIENTS]

CHECK (use substitution)

You can recognize a special case when ALL THE VARIABLES DISAPPEAR Possible Solutions of a Linear Equation Result What Does This Mean? How Many Solutions? You find an answer Special Case: IDENTITY Infinitely Many Solutions Variables disappear, both sides are the same All Real Numbers Result Ways to Solve a Linear System § GRAPHING Normal Case: Special Case: NO SOLUTIONS Variables disappear, sides are the different The SOLUTION to a linear system is the point of intersection, written as an ordered pair. It is also known as the BREAK EVEN POINT 0 Solutions No Solution How Many Solutions? Graphically? One Solution Lines Intersect Infinitely Many Same Lines (overlapping) No Solution Parallel Lines SPECIAL CASES § Time Consuming § Estimate (not always accurate) § Solution is the point of intersection § SUBSTITUTION § If a = b and b = c, then a = c § Best when both equations are in slope-intercept form § ELIMINATION § If a = b and c = d, then a + c = b + d § Best when both equations are in standard form LINEAR SYSTEMS

ALWAYS isolate the absolute value FIRST! NEVER distribute into absolute value! Absolute value equations usually have 2 answers! │stuff│= pos │stuff│= 0 │stuff│= neg 2 solutions 1 solution no solution When you switch the sign, you switch the symbol! switch sign switch symbol FORM: Variable/Symbol/Number Example: x > 7 not 7 < x When multiplying or dividing by a negative number you MUST flip the inequality symbol! Less th“and” where things overlap Great“or” everything together │stuff│≥ 0 │stuff│< 0 symbol > all real #s no solution < ≥ arrows ABSOLUTE VALUE INEQUALITIES ≤