Solving Linear Equations

And the Secret IS… When Solving Linear equations you must do the opposite That is what algebra is all about,,, …it’s doing the opposite.

Add = __________ Subtract = __________ Multiply = __________ Now another set. Add = __________ Subtract = __________ Multiply = __________ Divide = __________

Subtract Add = __________ Add Subtract = __________ Divide Your answers should have been… Subtract Add = __________ Add Subtract = __________ Divide Multiply = __________ Divide = __________ Multiply

+ = __________ - = __________ ( )( ) = __________ / = __________ One last set. + = __________ - = __________ ( )( ) = __________ / = __________

- ÷ x + = __________ + - = __________ ( )( ) = __________ Your answers should have been… - + = __________ + - = __________ ÷ ( )( ) = __________ x / = __________

One Step Equations Now you are going to work on solving some Algebra problems. Remember… ITS ALL ABOUT DOING OPPOSITE!!!

One Step Equations X + 3 = 17 What Side of the equation you are going to work with ? The Rights side The lefts side

One Step Equations X + 3 = 17 What Side of the equation you are going to work with ? The lefts side …Because that’s where the varible is.

One Step Equations X + 3 = 17 Click on the answer below that is the opposite . Add 3 Subtract 3 Multiply 3 Divide 3

One Step Equations Good Job! The correct answer is subtract 3.

One Step Equations 4x = 20 What Side of the equation you are going to work with ? The Rights side The lefts side

One Step Equations 4x = 20 What Side of the equation you are going to work with ? The lefts side …Because that’s where the variable is.

One Step Equations 4x = 20 Click on the answer below that is the opposite. Add 4 Subtract 4 Multiply by 4 Divide by 4

One Step Equations x 5 10 = What Side of the equation you are going to work with ? The Rights side The lefts side

One Step Equations x 5 10 = What Side of the equation you are going to work with ? The Rights side …Because that’s where the variable is.

One Step Equations x 5 10 = Click on the answer below that is the opposite . Add 5 Subtract 5 Multiply by 5 Divide by 5

One Step Equations Good! The correct answer is multiply by 5.

One Step Equations 8 = X – 7 What Side of the equation you are going to work with ? The Rights side The lefts side

One Step Equations 8 = X – 7 What Side of the equation you are going to work with ? The Rights side …Because that’s where the variable is.

One Step Equations 8 = X – 7 Click on the answer below that is the opposite of. + 7 - 7 x 7 ÷ 7

One Step Equations Congratulations!

One Step Equations Opposite! Alright, now you are going to actually solve some problems. This is nothing to be worried about, just remember one word… Opposite!

One Step Equations X + 5 = 13 What Side of the equation you are going to work with ? The Rights side The lefts side

One Step Equations X + 5 = 13 What Side of the equation you are going to work with ? The lefts side …Because that’s where the variable is.

One Step Equations X + 5 = 13 Click on the answer below that is the opposite. + 5 - 5 x 5 ÷ 5

X + 5 = 13 -5 -5 _________ One Step Equations You subtract – 5 in both side of the equatiion .

X + 5 = 13 - 5 - 5 _________ X = 8 One Step Equations - 5 - 5 X = 8 You drop down the X and equal sign. Cancel 5 Drop down “=“ sign. And then subtract 13 – 5 = 8.

One Step Equations 15 =X - 9 What Side of the equation you are going to work with ? The Rights side The lefts side

One Step Equations 15 =X - 9 What Side of the equation you are going to work with ? The Rights side …Because that’s where the variable is.

One Step Equations 15 =X - 9 Click on the answer below that is the opposite. + 9 - 9 x 9 ÷ 9

15 = X - 9 + 9 +9 _________ X 24 = One Step Equations You add + 9 in both side of the equation . Now add 15 + 9 gives you 24. You drop down “ =“ sign then X Cancel 9

One Step Equations 2x = 18 What Side of the equation you are going to work with ? The Rights side The lefts side

One Step Equations 2x = 18 What Side of the equation you are going to work with ? The lefts side …Because that’s where the variable is.

One Step Equations 2x = 18 Click on the answer below that is the opposite. + 2 - 2 x 2 ÷ 2

___ 2x = 18 __ _________ 2 2 1 x 9 = One Step Equations ÷ You divide by 2 in both side. Now 2 divide 2 gives you 1 x. You drop down “ =“ Now add 18 2 gives you 9. ÷

___ 2x = 18 __ _________ 2 2 1 x 9 = One Step Equations Do we really have to write the 1 in Front of the X. No.

One Step Equations 24 = 4x What Side of the equation you are going to work with ? The Rights side The lefts side

One Step Equations 24 = 4x What Side of the equation you are going to work with ? The Rights side …Because that’s where the variable is.

___ __ 24 = 4x _________ 6 = x 1 One Step Equations 4 4 ___ __ 24 = 4x _________ 4 4 6 = x 1 You divide by 4 in both side. Now 24 divide 4 gives you 6. You drop down “ =“ Now 4 divide 4 gives you 1 x.

___ __ 24 = 4x _________ 6 = x 1 One Step Equations 4 4 ___ __ 24 = 4x 4 _________ 4 6 = x 1 Do we really have to write the 1 in Front of the X. No.

One Step Equations x 3 = 12 What Side of the equation you are going to work with ? The Rights side The lefts side

One Step Equations x 3 = 12 What Side of the equation you are going to work with ? The lefts side …Because that’s where the variable is.

One Step Equations x 3 = 12 Click on the answer below that is the opposite. + 3 - 3 x 3 ÷ 3

x 3 3• = 12 •3 ___________ 1 x = 36 One Step Equations You multiply by 3 in both side. Now 3 divide 3 gives you 1X. You drop down “ =“ Now 12 multiply by 3 equals 36.

x 3 3• = 12 •3 ___________ 1 x = 36 One Step Equations Do we really have to write the 1 in Front of the X. No.

5X - 3 = 12 Two Steps Equations What Side of the equation you are going to work with ? The Rights side The lefts side

5X - 3 = 12 Two Steps Equations What Side of the equation you are going to work with ? The lefts side …Because that’s where the variable is.

5X - 3 = 12 Two Steps Equations What the first step you are going to do? add 3 then divide by 5 divide 5 then add by 3

5X - 3 = 12 Two Steps Equations What the first step you are going to do? add 3 then divide by 5

5X - 3 = 12 +3 +3 ___________ = 5X 15 Two Steps Equations You add by 3 in both side. You drop down 5x Cancel 3 You drop down = Now 12 plus 3 gives you 15.

5X - 3 = 12 ___________ +3 +3 = 5X __ 15 __ ___________ 5 5 1 x = 3 Two Steps Equations 5X - 3 = 12 ___________ +3 +3 = 5X __ 15 __ ___________ 5 5 1 x = 3 Now divide by 5 in both sides Now 5 divide 5 gives you 1X. You drop down “ =“ Now 15 divide by 5 equals 3

5X - 3 = 12 +3 +3 ___________ = 5X __ 15 __ ___________ 5 5 1 x = 3 Two Steps Equations 5X - 3 = 12 +3 +3 ___________ = 5X __ 15 __ ___________ 5 5 1 x = 3 Do we really have to write the 1 in Front of the X. No.

- 44= - 8 - 6X Two Steps Equations What Side of the equation you are going to work with ? The Rights side The lefts side

- 44= - 8 - 6X Two Steps Equations What Side of the equation you are going to work with ? The Rights side …Because that’s where the variable is.

- 44= - 8 - 6X Two Steps Equations What the first step you are going to do? add 8 then divide by -6 divide -6 then add by 8

- 44= - 8 - 6X Two Steps Equations What the first step you are going to do? add 8 then divide by -6

- 44 = - 8 - 6X +8 +8 ___________ - 6X -36 = Two Steps Equations You add + 8 in both side. Now -44 plus 8 gives you -36. You drop down “ =“ Cancel 8 Now You drop down -6x

- 44 = - 8 - 6X ___________ +8 +8 - 6X -36 __ = __ ___________ -6 -6 6 Two Steps Equations - 44 = - 8 - 6X ___________ +8 +8 - 6X -36 __ = __ ___________ -6 -6 6 = X Now divide by -6 in both sides Now -36 divide -6 gives you 6. Now -6 divide -6 gives you 1X.

3 ( 5 X – 3 ) = 21 _ ( 21 15 X ) = 9 The Distributive Property says that the number in front of the parentheses can be multiplied by each term in side the parentheses. Now 3 multiply by 5 equals 15 Add 3 multiply by 3 equals 9

3 ( 5 X – 3 ) = 21 _ ( ) 21 15 X = 9 Do you need the parenthesis ? No

3 ( 5 X – 3 ) = 21 _ 15 X = 21 9 _____________ + 9 + 9 = 15 X 30 = Add 9 in both sides You drop 15 X Cancel 9 Drop = sign Add 21 + 9 = 30

3 ( 5 X – 3 ) = 21 _ 15 X = 21 9 _____________ + 9 + 9 = 15 X _ 30 _ Divide 15 in both sides 15 divide by 15 equals 1 x

3 ( 5 X – 3 ) = 21 _ = 21 15 X 9 _____________ + 9 + 9 = 1 X 30 _ 15 = Divide 15 in both sides 15 divide by 15 equals 1 x

3 ( 5 X – 3 ) = 21 _ 15 X = 21 9 _____________ + 9 + 9 = 1 X 30 _ 15 = Divide 15 in both sides 15 divide by 15 equals 1 x 30 divide 15 = 2

3 ( 5 X – 3 ) = 21 _ 15 X = 21 9 _____________ + 9 + 9 = 1 X 30 _ 15 = Divide 15 in both sides 15 divide by 15 equals 1 x 30 divide 15 = 2

3 ( 5 X – 3 ) = 21 _ = 21 15 X 9 _____________ + 9 + 9 = 1 X 2 = Divide 15 in both sides 15 divide by 15 equals 1 x 30 divide 15 = 2

3 ( 5 X – 3 ) = 21 _ = 21 15 X 9 _____________ + 9 + 9 = 1 X 2 = Divide 15 in both sides 15 divide by 15 equals 1 x 30 divide 15 = 2

10X - 15 = 5X+10 -5X ______________ -5X Variables in Both Sides You subtract – 5x in both side.

10X - 15 = 5X+10 -5X ______________ -5X - 5X 15 = 10 Variables in Both Sides 10X - 15 = 5X+10 ______________ -5X -5X - 5X 15 = 10 Subtract 10X - 5X = 5X Drop - sign Drop 15 %X Drop = sign Cancel 5X Drop 10

10X - 15 = 5X+10 -5X ______________ -5X - 5X 15 = 10 +15 +15 Variables in Both Sides 10X - 15 = 5X+10 ______________ -5X -5X - 5X 15 = 10 +15 +15 ______________ Add + 15 in both side.

10X - 15 = 5X+10 -5X ______________ -5X - 5X 15 = 10 +15 +15 Variables in Both Sides 10X - 15 = 5X+10 ______________ -5X -5X - 5X 15 = 10 +15 +15 ______________ 25 5X = Drop the 5X Cancel 15 and Drop the = sign Add 10 + 15 = 25

10X - 15 = 5X+10 ______________ -5X -5X - 5X 15 = 10 +15 +15 Variables in Both Sides 10X - 15 = 5X+10 ______________ -5X -5X - 5X 15 = 10 +15 +15 ______________ 25 5X = __ __ 5 5 Divide by 5 in both side.

10X - 15 = 5X+10 ______________ -5X -5X - 5X 15 = 10 +15 +15 Variables in Both Sides 10X - 15 = 5X+10 ______________ -5X -5X - 5X 15 = 10 +15 +15 ______________ 25 5X = __ __ 5 5 1 X = 5

10X - 15 = 5X+10 ______________ -5X -5X - 5X 15 = 10 +15 +15 Variables in Both Sides 10X - 15 = 5X+10 ______________ -5X -5X - 5X 15 = 10 +15 +15 ______________ 25 5X = __ __ 5 5 1 X = 5

Congratulations We Finished