Solving

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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.


The inverse of add is SUBTRACT

The inverse of subtract is ADD

The inverse of multiply isThe inverse of divide is

DIVIDE

MULTIPLY+ → −

+→−× → ÷

×→÷


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

side to keep it balanced.

30 5 x 6=


To solve a multiplication equation Use the inverse operation for

multiplication which is division.

Get the variable alone, by dividing the same number into both sides.


Try to solve this multiplication equation.

56 8x=

How do you get x all by itself?


56 8x=

Divide 8 into both sides.

887


56 8x=


•7

Check your answer by substitution!


Try to solve this multiplication equation

42 7x=



42 7x=77

6



42 7x= •6

Divide 7 into both sides.Check your answer by substitution!


To Solve a Multiplication Equation

8x = 32 Get the variable alone.

8 8 Divide 8 into both sides.

x = 4 8 divided by 8 cancels out

8 • 4 = 32 Show your check!

Divide the same number into both sides

32 = 32 Finish your check!


1)

2)

3)

4)

5x 20=5x 20=

x 4=5 5

36 3y=36 3y=

12 y=3 3

24 8t=24 8t=

3 t=8 8

4k 18=4k 18=

18k4

=4 4

92

= 1or 42


To solve a division equation

Use the inverse operation for division which is multiplication.

Get the variable alone, by multiplying the same number to both sides.


Try to solve this division equation

x3 15

=



x3 15

=•3•3

Multiply both sides by 3

45


x3 15

=


45




x6 4

=



x6 4

=•6•6


24


x6 4

=


24




x7 -7

=



x7 -7

=•7•7


-49


x7 -7

=


-49



To Solve a Division EquationMultiply the same number to both sides.

= 25

Get the variable alone.

= 25 Multiply both sides by 3.

x = 75 3 divided by 3 cancels out to 1.

Show your check!

x 3x

3

253

=75

25 = 25Finish your check!

3• •3


-3x = 21-3 -3

x = -7

m = 8-2(-2) (-2)

m = -16

-3(-7) = 21 21 = 21

= 8-2

-16

8 = 8

Try These Equations Show your check!


Try These Equations

1) 2)x 43

=

3 x 43

3• = •

x 12=

m 105

=

5m 05

5 1• = •

m 50=


Try These Equations

3) 4)y

162

=

2y

62

2 1• = •

y 32=

k 74

=

4 k 74

4• = •

k 28=


Take Out Your Study Guide!!!


5x = 40 Get the variable alone.

5 5 Divide 5 into both sides.


5 • 8 = 40 Show your check!

Divide the same number into both sides

#5

40 = 40 Finish your check!


= 20

Get the variable alone.

= 20 Multiply both sides by 2.


Show your check!

x 2x

2

Multiply the same number to both sides

#6

4020

2=

20 = 20Finish your check!

2• •2


Teacher Note: The following slides may be inserted at the beginning of the lesson if the lesson is also teaching writing expressions and/or equations.


Addplus

sum

increased by

total

more than

added to

Subtractminus

difference

decreased by

less than

subtracted from

less

Multiplytimes

product of

twice ( )2•

Dividequotient

Flip Flop Numbers


Placement Rule Always write the variable

after the number! a 4 WRITE IT AS 4a


Using Parentheses8 x is written as

8(x) (8)x (8x) 8x

Parentheses mean

multiply!


Translate the following into equations.1) Eleven more than a number t is 23.

2) Eight times a number k is equal to 56.

3) Thirteen less m equals 6.

4) The quotient of x and 3 is 18.

t 11 23+ =

8k 56=

13 m 6− =

x 3 18÷ =


Four times the sum of m and 5 minus 3

Five minus twice the quotient of x and 8

The quotient of a and 7 minus 3

( )1) 4 m 5 3+ −

( )2) 5 2 x 8− ÷

3) a 7 3÷ −

Write a phrase that describes each variable expression below.


Teacher Note: The following slides may be inserted at the end of the lesson if the lesson is also teaching solving equations with

fractions.


Long Way Short Way2

63

x =

2

3

2

32

3

6

1x = ÷

Easier to multiply by the reciprocal!


Solve the division by multiplying by the reciprocal.


#7

210

3y =3

2⎛ ⎞⎜ ⎟⎝ ⎠

3

2⎛ ⎞⎜ ⎟⎝ ⎠

10 3

1 2y = •

Multiply both sides by the reciprocal of the fraction.

cancel out t .3 2

2 3o 1•

210

3y =

Multiply the numerators. Multiply the denominators.30

2y = Simplify15=


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Solving

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