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 Look for the DISTRIBUTIVE PROPERTY

STEPS REASON Given Look to COMBINE LIKE TERMS on the same side Distributive Property 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) STEPS REASON Given Distributive Property Combine Like Terms Addition Axiom of Equality Inverse Property of Addition / Combine Like Terms Addition Axiom of Equality Inverse Property of Addition Combine Like Terms / [CONSTANTS]

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

CHECK  (use substitution)

SPECIAL CASES LINEAR SYSTEMS You can recognize a special case when ALL THE VARIABLES DISAPPEAR 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  Possible Solutions of a Linear Equation Ways to Solve a Linear System GRAPHING 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 Result What Does This Mean? How Many Solutions? Normal Case: You find an answer Special Case: IDENTITY Variables disappear, both sides are the same Infinitely Many Solutions All Real Numbers 0 Solutions No Solution Special Case: NO SOLUTIONS Variables disappear, sides are the different Result How Many Solutions? Graphically? One Solution Lines Intersect Same Lines (overlapping) Infinitely Many No Solution Parallel Lines SPECIAL CASES LINEAR SYSTEMS

Example: x > 7 not 7 < x  ALWAYS isolate the absolute value FIRST!  NEVER distribute into absolute value!  Absolute value equations usually have 2 answers! │stuff│= pos 2 solutions │stuff│= 0 1 solution │stuff│= neg no solution  When you switch the sign, you switch the 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” “and” where things overlap  Great“or” “or” everything together │stuff│≥ 0 all real #s │stuff│< 0 no solution switch sign switch symbol symbol > < ≥ ≤ arrows ABSOLUTE VALUE INEQUALITIES