Exercise 32 Page 443

Use the Addition Property of Equality to eliminate the subtraction.

c=-1/12

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To solve the equation, we have to isolate c on one side. Using the Addition Property of Equality, we can add 56 to both sides of the equation. This will eliminate the negative number on the left-hand side and isolate c.

-5/6+c=-11/12

AddEqn

LHS+ 5/6=RHS+ 5/6

-5/6+c+ 5/6=-11/12+ 5/6

CommutativePropAdd

Commutative Property of Addition

-5/6+5/6+c=-11/12+5/6

ExpandFrac

a/b=a * 2/b * 2

-5/6+5/6+c=-11/12+10/12

AddFrac

Add fractions

c=-1/12

To check that this solution is correct, let's substitute c=- 112 into the original equation and simplify.

-5/6+c=-11/12

Substitute

c= -1/12

-5/6+( -1/12)=-11/12

AddNeg

a+(- b)=a-b

-5/6-1/12=-11/12

ExpandFrac

a/b=a * 2/b * 2

-10/12-1/12=-11/12

SubFrac

Subtract fractions

-11/12=-11/12 ✓

Because the left-hand side and right-hand side are equal, c=- 112 is the correct solution.

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