WHAT’S THE MISSING LETTER? WHAT’S THE MISSING LETTER?

OrOrHow to solve Algebraic How to solve Algebraic

EquationsEquations

4y + 4 – y + 3 + = y + 284y + 4 – y + 3 + = y + 28(they really won’t be this long) (they really won’t be this long)

But what’s this Algebra But what’s this Algebra stuff?stuff?

ALGEBRAALGEBRA

ALGEBRA means: ALGEBRA means: Reduction and Reduction and comparison (using numbers and letters).comparison (using numbers and letters).

It’s all about BALANCEIt’s all about BALANCE

In math, what you do to one side

you have to do to the other.

The Mystery “person” in The Mystery “person” in Algebra is the…Algebra is the…

VARIABLE (S): A letter(s) or symbol that VARIABLE (S): A letter(s) or symbol that represents a number in an algebraic represents a number in an algebraic expression. In y + 5 = 9 the expression. In y + 5 = 9 the variable variable is y. is y.

What’s the opposite What’s the opposite operation?operation?

INVERSE OPERATION: Two operations INVERSE OPERATION: Two operations that undo each other. Addition and that undo each other. Addition and subtraction undo each other. Multiplication subtraction undo each other. Multiplication and division undo each other.and division undo each other.

Let’s do some work. But Let’s do some work. But first…first…

The inverse of division is The inverse of division is ________________________.. MULTIPLICATIONMULTIPLICATION The inverse of subtraction is ___________. The inverse of subtraction is ___________. ADDITIONADDITION The inverse of multiplication is ___________. The inverse of multiplication is ___________. DIVISIONDIVISION The inverse of addition is ___________.The inverse of addition is ___________. SUBTRACTIONSUBTRACTION

Solving Subtraction Solving Subtraction EquationsEquations

x – 150 = 180x – 150 = 180

X – 150 + 150 = 180 + 150 (-150 +150 =0)

x = 330

X – 150 + 150 = 180 + 150 (-150 +150 =0)

x = 330 Try this on your whiteboard. Balance yours using the inverse Try this on your whiteboard. Balance yours using the inverse

operation. operation. y – 11 = 3y – 11 = 3

y – 11 y – 11 + 11+ 11 = 35 = 35 + 11+ 11 y = 46 The inverse operation was ______y = 46 The inverse operation was ______

ADDITIONADDITION

2) x + 8 = 272) x + 8 = 27 x + 8 x + 8 – 8– 8 = 27 = 27 – 8– 8 x = 19 The inverse operation was ____x = 19 The inverse operation was ____ SUBTRACTIONSUBTRACTION

What’s What’s next?...Multiplication!next?...Multiplication!

150x = 180150x = 180(Remember…if a number and a variable are stuck together, that means they are going to be…

+, -, x or ÷ ?

What’s What’s next?...Multiplication!next?...Multiplication!

150x = 180150x = 180 (Remember…if a number and a variable are stuck

together, that means they are going to be… +, -, x or ÷ ?

150x = 180150x = 180

150 x150 x = = 180180 150 150150 150

150 150 180180 x = 1.2x = 1.2

Try some. Use the Inverse Try some. Use the Inverse Operation.Operation.

4b = 324b = 32 4b 4b = = 32 32 44 32 32

4 44 4 b = 8 (4 b = 8 (4 •• 8 = 32) 8 = 32)

48 = 6y48 = 6y

48 48 = = 6y 6y 66 48 48 6 66 6

Y = 8 (6 Y = 8 (6 •• 8 = 48) 8 = 48)

The inverse of The inverse of multiplication is…multiplication is…

DIVISION!!!DIVISION!!!

And finally, DivisionAnd finally, Division

The inverse of Division is…The inverse of Division is… MULTIPLICATION.MULTIPLICATION.

X ÷ X ÷ 150 150 = 180= 180

X ÷ X ÷ 150 150 = 180= 180

X ÷ X ÷ 150 150 •• 150 150 = 180 = 180 •150•150 (÷ (÷ 150 150 •• 150 150 cancel out) cancel out) X = 27000X = 27000

Two more examples. Two more examples. Remember to show the Remember to show the

inverse operationinverse operation. . c c ÷ 3 = 9÷ 3 = 9 c c ÷ 3 ÷ 3 • 3• 3 = 9 = 9 • 3• 3 C = 27 (9 C = 27 (9 • 3• 3 ) )

2.5 = z ÷ 42.5 = z ÷ 4 2.5 2.5 • 4• 4 = z ÷ 4 = z ÷ 4 • 4• 4 10 = z (2.5 10 = z (2.5 • 4• 4) )

One more step…Combining like One more step…Combining like termsterms

m + 6 + 12 = 38m + 6 + 12 = 38 Combine the numbers firstCombine the numbers first +6 + 12 = 18+6 + 12 = 18 M +18 = 38M +18 = 38 Now do the inverse operationNow do the inverse operation M + 18 – 18 = 38 – 18M + 18 – 18 = 38 – 18 M = 20M = 20

What if…?What if…?

3 + y – 7 = 453 + y – 7 = 45 You can do each inverse as you go.You can do each inverse as you go. 3 3 – 3– 3 + y – 7 + y – 7 +7+7 = = 45 45 – 3 + 7– 3 + 7 Y = (45Y = (45-3-3) ) + 7+ 7 Order of operations Order of operations Y = 42 Y = 42 + 7+ 7 Y = 49 3 + 49 – 7 = 45Y = 49 3 + 49 – 7 = 45

4 + p + 8 = 194 + p + 8 = 19