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Multiplication Property of Equality

When addition and multiplication are mixed in problems we will first apply the Addition Property vertically using a pattern (or balance beam ), where we work on each side of the equation at the same time. When we get to the step where there is a constant on one side and a variable multiplied by a coefficient not equal to one we will apply the Multiplication Property.

2.3a.Constant multiplied on both sides:

A x = B or A = B x

(A, B are letters to represent integers.)

Recall that

2.3b Find the variable x. To solve the equation we will keep the variable x on that side of the equation and move the constant to the other side. To do this multiply reciprocals to the entire equation or (both sides of the equation). First look at the pattern then follow the same steps through the example below.

 

Solving Equations using the Multiplication Property of Equality

Pattern:

Solve Multiply recip:
  Distributive Property
  Associative Property
Then Since

 

Example1

Solve Multiply recip:
  Distributive Property
  Associative Property
Then Recall
Check: Replace x with and simplify.

2.3c.Constant multiplied on both sides:

(A, B are letters to represent fractions.)

Recall that

i) Simplify the equation so that there are only integers on both sides

2.3d. Find the variable x. To solve the equation we will keep the variable x on that side of the equation and move the constant to the other side. To do this multiply reciprocal fractions to the entire equation or (both sides of the equation). First look at the pattern then follow the same steps through the example below.

 

 
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