Exercise 19 Page 22

To solve an equation, we should first gather all of the variable terms on one side and all of the constant terms on the other side using the Properties of Equality. In this case, we need to start by using the Distributive Property to simplify the right-hand sides of the equation. Now, we can continue to solve using the Properties of Equality.

1/6d+2/3=1/4d-1/2

SubEqn

LHS-1/6d=RHS-1/6d

1/6d+2/3-1/6d=1/4d-1/2-1/6d

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Simplify

ExpandFrac

a/b=a * 3/b * 3

1/6d+2/3-1/6d=3/12d-1/2-1/6d

ExpandFrac

a/b=a * 2/b * 2

1/6d+2/3-1/6d=3/12d-1/2-2/12d

SubFrac

Subtract fractions

2/3=1/12d-1/2

AddEqn

LHS+1/2=RHS+1/2

2/3+1/2=1/12d-1/2+1/2

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Simplify

ExpandFrac

a/b=a * 2/b * 2

4/6+1/2=1/12d-1/2+1/2

ExpandFrac

a/b=a * 3/b * 3

4/6+3/6=1/12d-1/2+1/2

AddFrac

Add fractions

7/6=1/12d

MultEqn

LHS * 12=RHS* 12

7/6* 12=1/12d* 12

MoveRightFacToNum

a/c* b = a* b/c

84/6=12/12d

CalcQuot

Calculate quotient

14=d

RearrangeEqn

Rearrange equation

d=14

The solution to the equation is d=14. We can check our solution by substituting it into the original equation.

1/6d+2/3=1/4(d-2)

Substitute

d= 14

1/6( 14)+2/3 ? = 1/4( 14-2)

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Simplify

SubTerm

Subtract term

1/6(14)+2/3 ? = 1/4(12)

MoveLeftFacToNumOne

a* 1/b= a/b

14/6+2/3 ? = 12/4

ExpandFrac

a/b=a * 2/b * 2

14/6+4/6? = 12/4

AddFrac

Add fractions

18/6 ? = 12/4

CalcQuot

Calculate quotient

3=3

Since the left-hand side is equal to the right-hand side, our solution is correct.