Exercise 27 Page 443

To solve the equation, we have to isolate r on one side. Using the Addition Property of Equality, we can add 34 to both sides of the equation. This will eliminate subtraction on the right-hand side and isolate r.

-1/3=r-3/4

AddEqn

LHS+ 3/4=RHS+ 3/4

-1/3+ 3/4=r-3/4+ 3/4

ExpandFrac

a/b=a * 4/b * 4

-4/12+3/4=r-3/4+3/4

ExpandFrac

a/b=a * 3/b * 3

-4/12+9/12=r-3/4+3/4

AddFrac

Add fractions

5/12=r

RearrangeEqn

Rearrange equation

r=5/12

To check that this solution is correct, let's substitute r= 512 into the original equation and simplify.

-1/3=r-3/4

Substitute

r= 5/12

-1/3? = 5/12-3/4

ExpandFrac

a/b=a * 3/b * 3

-1/3? = 5/12-9/12

SubFrac

Subtract fractions

-1/3? =-4/12

ReduceFrac

a/b=.a /4./.b /4.

-1/3=-1/3 ✓

Because the left-hand side and right-hand side are equal, r= 512 is the correct solution.