Multiplication Property of Equality MATH 018 Combined Algebra S. Rook

Overview • Section 2.2 in the textbook – Using the Multiplication Property of Equality – Solving more Complex Equations 2

Using the Multiplication Property of Equality

Using the Multiplication Property of Equality • When the variable is being multiplied by a number: – What’s the opposite operation of multiplication?

– Divide

BOTH SIDES

by the number

INCLUDING THE SIGN

•

Performing operations on only one side is a common mistake!

–

“What you do to one side, you must do to the other”

•

Dividing by the opposite sign is a common mistake!

– Remember the object is to isolate the

positive

variable!

– How would we solve 9

x

= 18 4

Using the Multiplication Property of Equality (Example)

Ex 1:

Solve: a) -

y

= 4 b) -12

z

= 8 5

Solving More Complex Equations

Solving More Complex Equations • To solve more complex equations: – Apply the distributive property if possible – Combine any like terms – Isolate the variable on one side of the equation – Apply the Addition Property of Equality – Apply the Multiplication Property of Equality – Don’t forget to simplify – Check 7

Solving More Complex Equations (Example)

Ex 2:

Solve – simplify fractions if necessary: a) 5

x

– 3

x

+ 3 = 19 + 4 – 6

x

b) 2(

y

– 3) + 6

y

= 9 – (

y

– 3) c) 4(

z

+ 1) – (2

z

– 4) = -1 8

Summary • After studying these slides, you should know how to do the following: – Use the Multiplication Property of Equality – Solve more complicated equations • Additional Practice – See the list of suggested problems for 2.2

• Next lesson – Further Solving Linear Equations (Section 2.3) 9