solving 2 step equations

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to one side of an equation,When you do something

91x1


91x1

you have to do exactlythe same thing

to the other side.

18x


To solve an equation means

to find every number that makes the equation

true.


In the equation,

x is the number

157 x

to get 15.

you add to 7


157 xWhat is the number?

8, of course. So we would write the solution

x = 8


In some equations, the solution is obvious.

55 x10x


But in other equations, the solution is not so obvious.

10122 x


10122 x

Many times we needa way to solve equations.

Especially if there is more than one step to solve.


1) Undo the addition or subtraction operation first, by using inverse operations.2) Undo the multiplication or division operation second, by using inverse operations.


REMEMBER


To solve any equation, you want to get the variable all by itself. You get the variable alone by using inverse operations.

Inverse Operations are like Opposites.


I am going to show you 2 ways to solve this equation.

Hard way Easy wayUndo Multiplication or Division 1st

Undo Addition or Subtraction 1st

3x + 4 = 16


Hard way Easy way Undo Multiplication or Division 1st Undo Addition or

Subtraction 1st 3x + 4 = 163 3

3x3

+ 43

= 163

- 43

- 43

x + 43

= 163

x = 123

x = 4

3x + 4 = 16 -4 -4

3x = 123 3

x = 4


1) GOAL:Get the variable on one side of the equation.

2) You always perform the same operation toboth sides of an equation.

3) To undo an operation you perform its opposite operation to both sides of the equation.4) It is easier if you undo addition or subtraction before you undo multiplication or division.


2x + 4 = 10 Get the variable alone.

- 4 - 4 Subtract 4 from both sides.

2x = 6 +4 and -4 cancel out__ __ 2 2

Divide both sides by 2 x = 3

Show your check. 2(3) +4 = 10

Finish your check.6 + 4 = 10 10 = 10

2 divided by 2 cancel to 1


3m - 10 = 17 Get the variable alone. + 10 +10 Add 10 to both sides.

3m = 27 +10 and -10 cancel out__ __ 3 3

Divide both sides by 3 m = 9

Show your check. 3(9) – 10 = 17

Finish your check.27 – 10 = 17 17 = 17



– 4 = 8

Get the variable alone.

3 ( ) = 3 12 Multiply both sides by 3.

x = 36 3 divided by 3 cancel to 1

x 3

x 3

+4 +4 Add 4 to both sides.x 3

= 12 + 4 and -4 cancel out.

– 4 = 8

36 3

12 – 4 = 8

8 = 8

Show your check.

Finish your check.


+ 6 = 14


2 ( ) = 2 8 Multiply both sides by 2.

x = 16 2 divided by 2 cancel to 1

x 2

x 2

- 6 - 6 Subtract 6 from both sides.x 2

= 8 + 6 and -6 cancel out.

+ 6 = 14

16 2

8 + 6 = 14

14 = 14

Show your check.

Finish your check.


What Operation Do You Do?

1) 3x + 8 = 24 Subtract 8

2) 5x - 10 = 19

Divide by 3FIRST SECOND

Add 10 Divide by 5

3) x - 4 = 20

2

Add 4 Multiply by 2

4) - 30 = -5x + 5 Subtract 5 Divide by -5


3 3

1) 2x 5 19 x2) 15 63

5 5 2x 242 2x 12

15 15 x 93

x 27


3) 8x 1 25 x4) 4 35

1 1

8x 248 8

x 3

5 5

4 4 x 75

x 35


Think about what you need to do to isolate the variable.

Get rid of addition or subtraction first. Second get rid of multiplication or division.


The End!Take out your study guide!


1) Undo the addition or subtraction operation first, by using inverse operations.

2) Undo the multiplication or division second, by using inverse operations.

#11


2 Step Subtract/Multiply Equation

3m - 10 = 17 Get the variable alone.

+10 +10 Add 10 to both sides.

3m = 27 +10 and -10 cancel out__ __ 3 3 Divide both sides by 3

m = 9

#12

Show your check. 3(9) – 10 =17

Finish your check.27 – 10 =17 17 =17



+ 6 = 14


( ) = 8 Multiply both sides by 2.

x = 16 2 divided by 2 cancels out

x 2

x 2

- 6 - 6 Subtract 6 from both sides.x 2

= 8

#13

+ 6 and -6 cancel out.

+ 6 = 14

16 2

8 + 6 = 14

14 = 14

Show your check.

Finish your check.

2 2


TEACHER NOTE: Use the following slides the next day when correcting homework.


HOMEWORK EXPLANATION


An Equation is like a balance scale. Everything must be equal

on both sides.

20 2x +5=


20 2x +5=

What you do to one side of an equation, you must do to the

other side to keep it balanced!

-5-5


15 2x =



__2

__2


7.5 x =




Try to solve this subtraction equation

18 n - 3=

How do you get n all by itself?

+3+3


Try to solve this subtraction equation

21 n =

How do you get n all by itself?


Show your check by substituting your answer back into the original

equation.

18 n - 3=

21


Try to solve this division equation

x3 15

=

How do you get x all by itself?

•3•3


Try to solve this division equation

x45

=

How do you get x all by itself?


SHOW YOUR CHECK!

x3 15

=45


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