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SOLVING

2 STEP

ALGEBRAIC EQUATIONS

PART 2

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INVERSE OPERATIONS

+

-

x

÷

x2

√

SAME NUMBER

OPPOSITE OPERATION

LAST WEEK’S FOCUS

THIS WEEK’S FOCUS

3 of 33

= $100

= $200

= $300

m

m

m

m

m

m

WHAT IS AN EASIER WAY TO WRITE MULTIPLE “m” VARIABLES?

3m

2m

1m

BUT… 1m isn’t easier than just writing “m"

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Multiple Variables

  • A number in front of a variable indicates how many of that value there are
  • The number is ALWAYS written in front (before) of the variable (not after)
  • When there is NO number in front of a variable, that means there is only 1 of that value

m

2m

3m

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m

m

m

3m

$100

+$100

+$100

= $300

OR

(faster)

$100

x 3

= $300

3m

3(100)

= $300

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Multiple Variables

  • When a number is next to a variable this is a MULTIPLICATION operation

m

2m

3m

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4 = n

+ 3

LEFT SIDE

RIGHT SIDE

LAST WEEK

8 of 33

RIGHT SIDE

LEFT SIDE

n

+3

4 = n

+ 3

LAST WEEK

WE NEED TO GET ”n” BY ITSELF

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15 = 6n

+ 3

LEFT SIDE

RIGHT SIDE

10 of 33

RIGHT SIDE

LEFT SIDE

n

n

n

n

n

n

+3

15 = n

+ 3

WE NEED TO GET A SINGLE ”n” BY ITSELF

-3

SAME NUMBER

OPPOSITE OPERATION

6

BUT WE CAN’T JUST GET RID OF THAT “6” BECAUSE WE SAY SO

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This is called:

  • “Solving an equation”
  • “Isolating a variable”

​

I CALL IT…

  • “Math Murder”

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INVERSE OPERATIONS

+

-

x

÷

x2

√

SAME NUMBER

OPPOSITE OPERATION

LAST WEEK’S FOCUS

THIS WEEK’S FOCUS

13 of 33

Multiple Variables

  • When a number is next to a variable this is a MULTIPLICATION operation

m

2m

3m

14 of 33

RIGHT SIDE

LEFT SIDE

n

n

n

n

n

n

+3

15 = n

+ 3

WE NEED TO GET A SINGLE ”n” BY ITSELF

-3

SAME NUMBER

OPPOSITE OPERATION

6

÷6

SAME NUMBER

OPPOSITE OPERATION

BUT WAIT!!!!!

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ALGEBRA RULE #1

WHAT YOU DO TO ONE SIDE YOU MUST DO TO THE OTHER!

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RIGHT SIDE

LEFT SIDE

n

n

n

n

n

n

+3

15 = n

+ 3

WE NEED TO GET A SINGLE ”n” BY ITSELF

-3

SAME NUMBER

OPPOSITE OPERATION

6

-3

SAME NUMBER

OPPOSITE OPERATION

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RIGHT SIDE

LEFT SIDE

n

n

n

n

n

n

12 = n

WE NEED TO GET A SINGLE ”n” BY ITSELF

6

÷6

SAME NUMBER

OPPOSITE OPERATION

÷6

SAME NUMBER

OPPOSITE OPERATION

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RIGHT SIDE

LEFT SIDE

n

2 = n

÷6

SAME NUMBER

OPPOSITE OPERATION

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n

Why is 1 variable left over?

3 – 3 = 0

DOES:

6 ÷ 6 = 0 ?

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ANY NUMBER DIVIDED BY ITSELF =

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a

a

a

a

-9

23 = a

-9

WE NEED TO GET A SINGLE ”a” BY ITSELF

+9

SAME NUMBER

OPPOSITE OPERATION

4

+9

SAME NUMBER

OPPOSITE OPERATION

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a

a

a

a

32

4

÷4

SAME NUMBER

OPPOSITE OPERATION

= a

÷4

SAME NUMBER

OPPOSITE OPERATION

8

23 of 33

a

a

a

a

-9

8 = a

8

8

8

8

23 = a

-9

4

=8+8+8+8-9

23

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THEN:

  1. Write the Equation
  2. Sub the Variables
  3. BEDMAS (Do the math)
  4. BEDMAS
  5. BEDMAS
  6. SAMDEB

​

LINE IT UP (Line up your equal signs)

(BEDMAS BACKWARDS to SOLVE)

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  1. 5a + 6 = 41

​

  • 15b + 402 = 447

​

  • 6 422 + 2c = 6 525

TRY IT

d) 10d – 65 = 15

​

e) 3e – 323 + (45 – 3) = -215

​

f) 6f - 52 = 12 – 32 + 2

26 of 33

SQUARE DANCE

SHOWDOWN

1

2

27 of 33

MATH GAME

28 of 33

ROUND 1:

29 of 33

ROUND 2:

30 of 33

MATH JOURNAL

MATH�GAME

INDEPENDENT WORK

TECH�CENTRE

Aliya

Janagan

Cianna

Katerina

Marissa

Indiya

Korraugh

Anson

Ariella

Ayesha

Aysia

Alize

Tishaunn

Aniya

Makayla

Niara

Pari

Rameen

Veronica

Aerin

Deepthi

Jasmine

Jeffrey

Nathan

Shafeeq

Alyson

Alyssa

Houston

Jayce

Mkwasi

Sar-alty

Sue

MRSTAV

GUIDED

WITH STAV

1 2 3 4 5

31 of 33

MATH JOURNAL

MATH�GAME

INDEPENDENT WORK

TECH�CENTRE

Colton

Chloe

Jamila

Najaela

Peach

​

Anousha

Beatrice

Cameron

Dominic

Zachary

​

Annika

Mini Strach

Somaya

Talia

Victoria

Ruthie

Demi

Elicia

Greyson

Jaylan

Yonge

To Uyen

Cody

Jaime

Nevaeh

Noah

Stella

Xzavior

MRSTAV

GUIDED

WITH STAV

1 2 3 4 5

32 of 33

S+202-2÷(42+84)-(4+T) = A+V2+(4+T+A+V+52)�S+202-2÷(42+84)-(4+10) = 2+52+(4+10+2+5+52)�S+202-2÷(16+4096)-(4+10) = 2+52+(4+10+2+5+25)�S+202-2÷4112-14 = 2+25+46�S+202-0.000486381323-14 = 2+25+46�S+187.9995136187- 187.9995136187 = 73-187.9995136187�S = -114.9995136187�S = -115�

Solve for S, when T = 10, A = 2, V = 5

BEDMAS

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S+202-2÷(42+84)-(4+T) = A+V2+(4+T+A+V+52)�

Solve for S, when T = 10, A = 2, V = 5

BEDMAS