Exercise 37 Page 106

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 left-hand side of the equation.

1/2h+1/3(h-6)=5/6h+2

Distr

Distribute 1/3

1/2h+1/3h-1/3(6)=5/6h+2

▼

Simplify

MoveRightFacToNum

a/c* b = a* b/c

h/2+h/3-6/3=5h/6+2

CalcQuot

Calculate quotient

h/2+h/3-2=5h/6+2

ExpandFrac

a/b=a * 3/b * 3

3h/6+h/3-2=5h/6+2

ExpandFrac

a/b=a * 2/b * 2

3h/6+2h/6-2=5h/6+2

AddFrac

Add fractions

3h+2h/6-2=5h/6+2

AddTerms

Add terms

5h/6-2=5h/6+2

Now we can continue to solve using the Properties of Equality.

5h/6-2=5h/6+2

SubEqn

LHS-5h/6=RHS-5h/6

5h/6-2-5h/6=5h/6+2-5h/6

SubTerms

Subtract terms

-2 = 2 *

Simplifying the equation resulted in a contradiction. Therefore, the equation has no solution.