NAME:___________________________ Math8,Period1and2Mr.Rogove Date:__________

G8M4L3d:SolvingLinearEquationswithVariablesonBothSidesoftheEqualSign1

Learning Objective:Wewillsolvelinearequationswithvariablesonbothsidesoftheequalsign.(G8M4L3d)Concept Development: FourPropertiesofEqualityareusedinsolvinglinearequations

Addition Property of Equality If ! = !, then ! + ! = ! + !

Examples:

If ! − 2 = 7, then ! − 2+ 2 = 7+ 2

Subtraction Property of Equality If ! = !, then ! − ! = ! − !

Examples:

If ! + 3 = 18,

then ! + 3− 3 = 18− 3

Multiplication Property of Equality If ! = !, then ! × ! = ! × !

Examples:

If 13 ! = 6,

then 13 ! × 3 = 6 × 3

Division Property of Equality

If ! = ! !"# ! ≠ 0 , then!! =!!

Examples:

If 3! = 12,

then 3!3 = 123

SolvingEquations:ReviewandTips

• Whensolvinganequation,yourultimategoalisto“solveforx”or“isolatethevariable.”Youwillperformasequenceofmovesinordertogetyourvariabletoequaltoaconstantterm.

• Itwilloftenbeeasiertocombineliketermsandgetsimplerexpressionsoneachsideofyourequationpriortobeginningyourmathmoves.

• Youmustkeepbothsidesofyourequation(oneithersideoftheequalsign)inbalance.Seepropertiesofequalityabove.

NAME:___________________________ Math8,Period1and2Mr.Rogove Date:__________

G8M4L3d:SolvingLinearEquationswithVariablesonBothSidesoftheEqualSign2

Guided Practice: StepsforSolvingLinearEquationswithVariablesonBothSides1.Usethepropertiesofequalitytogetallofyourvariabletermsononesideoftheequation,andyourconstanttermsontheotherside.2.Combineliketerms.3.Usethepropertiesofequalitytoisolateyourvariable.4.Checkyoursolution.

2! − 3 = 4!

! − 8 = 5!

3! − 21 = ! + 15

4! + 11 = 2! + 25

NAME:___________________________ Math8,Period1and2Mr.Rogove Date:__________

G8M4L3d:SolvingLinearEquationswithVariablesonBothSidesoftheEqualSign3

! + 6+ ! + 8 = −26− 2!

5! + 13+ ! = 1− 9! + 42

−4 3! − 6 = 2 ! + 28 + 2!

2 3! − 2 = 2! − 1+ !

NAME:___________________________ Math8,Period1and2Mr.Rogove Date:__________

G8M4L3d:SolvingLinearEquationswithVariablesonBothSidesoftheEqualSign4

13 ! − 5 = ! − 171

14 ! + 18 = !

Closure: Isthereamistake?Ifso,where?

Step# Equation 2! − 3− 8! = 14+ 2! − 1

1 −6! − 3 = 2! + 13

2 −6! − 3+ 3 = 2! + 13+ 3

3 −6! = 2! + 16

4 −6! + 2! = 16

5 −4! = 16

6 −4!

−4 = 16−4

7 ! = −4

NAME:___________________________ Math8,Period1and2Mr.Rogove Date:__________

G8M4L3d:SolvingLinearEquationswithVariablesonBothSidesoftheEqualSign5

Independent Practice:

3! + 2− ! = 11! + 20

12 ! + 10 =

14 ! + 54

29− 3! = 5! + 5

3 ! + 10 + 4! = 6 4! − 1 + 2

NAME:___________________________ Math8,Period1and2Mr.Rogove Date:__________

G8M4L3d:SolvingLinearEquationswithVariablesonBothSidesoftheEqualSign6

Teacher Notes: Lesson4inENYMod4HW:KhanSolvingEVBS