1. SOLVING EQUATIONS
8.EE.7

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

3. 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

4. STEPS REASON Given Look for the DISTRIBUTIVE PROPERTY

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

6. 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 /

7. 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]

8. / / / 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]

9. CHECK  (use substitution)

10. 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

11. 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 solutions
│stuff│= 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│≥ all real #s
│stuff│< no solution
switch sign
switch symbol
symbol
>
< ≥ ≤
arrows
ABSOLUTE VALUE
INEQUALITIES