equations

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EquationsAn equation is a mathematical statement that shows 2 quantities are equal. An equation contains an equal sign.

#1

12 – 3 = 9 Numerical 3a = 30 Algebraic

To solve any equation use inverse operations.Your goal is to get the variable all by itself.


SOLUTION

A solution is the final answer to anequation, or the value of the variable.

#2

Example: 3a = 30 a = 10 10 is the solution


m + 8 = 12 Get the variable alone. – 8 –8 Subtract 8 from both sides.

m = 4 +8 and -8 cancel each other out.

4 + 8 = 12 Show your check.

Subtract the same number from both sides.

#3

12 = 12 Finish your check!


a – 15 = 22 Get the variable alone.

+15 +15 Add 15 to both sides.

a = 37 +15 and -15 cancel out

37 - 15 = 22 Show your check!

Add the same number to both sides.

#4



5x = 40 Get the variable alone.

5 5 Divide 5 into both sides.

x = 8 5 divided by 5 cancels out to 1.

5 • 8 = 40 Show your check!

Divide the same number into both sides

#5



= 20

Get the variable alone.

= 20 Multiply both sides by 2.

x = 40 2 divided by 2 cancels out to 1.

Show your check!

x 2x

2

Multiply the same number to both sides

#6

4020

2

20 = 20Finish your check!

2• •2


a – -3 = 21 Get the variable alone.

+ -3 + -3 Add -3 to both sides.

a = 18 + -3 and – -3 cancel out

18 - -3 = 21 Check your answer

Use inverse operations to solve integer equations.

#7

Finish your check 21 = 21


-8x = -64 Get the variable alone.

-8 -8 Divide -8 into both sides.

x = 8 -8 divided by -8 cancel out to 1.

-8 8 = -64 Check your answer.

Divide the same number into both sides

#8

Finish your check. -64 = -64


Algebra Tile Equations

2x + 2 = 4

#9

+ +

+ +

Take away 2 from both sides.

Divide both sides in half. 2x = 2

2 2 x = 1

=

Algebra2x + 2 = 4 -2 = -2

x

x Draw a picture.

+ +


Algebra Balance Scales#10

+ + + +

x

x

x

+ + + +

2) Take away 2x from both sides.

3) Take away 4 from both sides.

6 = 1x + 4-4 -4

2 = x

=

2x + 6 = 3x + 4 1) Draw a picture.

x

x

Algebra2x + 6 = 3x + 4 -2x = -2x

+ +


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

3 divided by 3 cancel to 1


+ 6 = 14

Get the variable alone.

( ) = 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


1) Goal: Isolate the variable.

2) Undo operations with their opposite operation.

3) Always do the same thing to both sides of the equation.

#14

4) Easiest to undo add/subtract before multiply/divide.


#15

1) 5x 2x 6 21

3x 6 21 6 6

3x 153 3

x 5

2) 6x 7 x 18

5x 7 18 7 7 5x 255 5

x 5

Solve Multi Step Equations


3x + 4 = 5x - 10-3x -3x

4 = 2x - 10+10 +10

14 = 2x2 27 = x

#16

Steps 1) Get all of the x’s on 1 side.

2) Subtract 3x from both sides.

3) Add 10 to both sides.

4) Divide both sides by 2


3 - 2x = 11

-3 -3 - 2x = 8 __ __

-2 -2 x = -4

#17

1)Get the variable alone, even if the coefficient is negative.

2)Subtract 3 from both sides.

3) +3 and -3 cancel out

4) Divide both sides by - 2

5) -2 divided by –2 cancel out

6) Show your check.

7) Finish your check.

3 - 2(-4) = 11

3 + 8 = 11

11 = 11


#18

+ + x

x x

–

Move the smaller

number of x’s to one side

2 = 2x - 2 +2 +2

4 = 2x

=

2x + 2 = 4x – 2

x

x

2x + 2 = 4x - 2 -2x -2x

x –

+ + ++

2 22 = x


#19

1) Get rid of the parenthesis by distributing

2) Combine like terms

3) Move the smaller number of x’s to one side

4) Move all numbers to the other side

5) Get x all by itself

6) Check your answer in the original equation

Circle answer. Show work in the check!


5(m - 6) = 10

5m - 30 = 10 + 30 +30

5m = 40

5 5m = 8

Get rid of parenthesis first by distributing.

#20

Check

in

the

original

equation!

5(8 - 6) = 10

Do

PEMDAS

in the

check! 5(2) = 10

10 = 10


8x - 4 = 3(2x + 8) Get rid of the parenthesis.8x - 4 = 6x + 24 Get the variables on one side.

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

6x and –6x cancel out2x - 4 = 24

Add 4 to both sides. + 4 + 4

x = 14 Divide both sides by 2.

2x = 28__ __ 2 2

#21

Show your check! 8(14) - 4 = 3(2 14+8)112 - 4 = 3(36) 108 = 108 Finish your check!


Extra


Equations An equation is a mathematical

statement that shows 2 quantities are equal. An equation contains an equal sign.

#1

12 – 3 = 9 Numerical3a = 30 Algebraic


#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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