WHAT’S THE MISSING LETTER? Or How to solve Algebraic Equations 4y + 4 – y = y + 28 (they really won’t be this long)

But what’s this Algebra stuff?

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

It’s all about BALANCE In math, what you do to one side you have to do to the other.

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

What’s the opposite operation? INVERSE OPERATION: Two operations that undo each other. Addition and subtraction undo each other. Multiplication and division undo each other. INVERSE OPERATION: Two operations that undo each other. Addition and subtraction undo each other. Multiplication and division undo each other.

Let’s do some work. But first… The inverse of division is ____________. The inverse of division is ____________. MULTIPLICATION MULTIPLICATION The inverse of subtraction is ___________. The inverse of subtraction is ___________. ADDITION ADDITION The inverse of multiplication is ___________. The inverse of multiplication is ___________. DIVISION DIVISION The inverse of addition is ___________. The inverse of addition is ___________. SUBTRACTION SUBTRACTION

Solving Subtraction Equations x – 150 = 180 X – = ( =0) x = 330

X – = ( =0) x = 330 Try this on your whiteboard. Balance yours using the inverse operation. Try this on your whiteboard. Balance yours using the inverse operation. y – 11 = 3 y – 11 = 3 y – = y – = y = 46 The inverse operation was ______ y = 46 The inverse operation was ______ ADDITION ADDITION 2) x + 8 = 27 2) x + 8 = 27 x + 8 – 8 = 27 – 8 x + 8 – 8 = 27 – 8 x = 19 The inverse operation was ____ x = 19 The inverse operation was ____ SUBTRACTION SUBTRACTION

What’s next?...Multiplication! 150x = 180 (Remember…if a number and a variable are stuck together, that means they are going to be… +, -, x or ÷ ?

What’s next?...Multiplication! 150x = 180 (Remember…if a number and a variable are stuck together, that means they are going to be… +, -, x or ÷ ?

150x = x = x = 1.2

Try some. Use the Inverse Operation. 4b = 32 4b = 32 4b = b = b = 8 (4 8 = 32) b = 8 (4 8 = 32) 48 = 6y 48 = 6y 48 = 6y = 6y Y = 8 (6 8 = 48) Y = 8 (6 8 = 48)

The inverse of multiplication is… DIVISION!!! DIVISION!!!

And finally, Division The inverse of Division is… The inverse of Division is… MULTIPLICATION. MULTIPLICATION. X ÷ 150 = 180 X ÷ 150 = 180

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

Two more examples. Remember to show the inverse operation. c c ÷ 3 = 9 c ÷ 3 3 = 9 3 C = 27 (9 3 ) 2.5 = z ÷ = z ÷ = z (2.5 4)

One more step…Combining like terms m = 38 m = 38 Combine the numbers first Combine the numbers first = = 18 M +18 = 38 M +18 = 38 Now do the inverse operation Now do the inverse operation M + 18 – 18 = 38 – 18 M + 18 – 18 = 38 – 18 M = 20 M = 20

What if…? 3 + y – 7 = y – 7 = 45 You can do each inverse as you go. You can do each inverse as you go. 3 – 3 + y – 7 +7 = 3 – 3 + y – 7 +7 = 45 – – Y = (45-3) + 7 Order of operations Y = (45-3) + 7 Order of operations Y = Y = Y = – 7 = 45 Y = – 7 = 45

4 + p + 8 = p + 8 = 19