Exercise 21 Page 131

To solve the equation, we have to isolate p on one side. Using the Addition Property of Equality, we will add 3 16 to both sides of the equation. This will eliminate the subtraction and isolate p.

p - 3 16 = - 2 12

AddEqn

LHS+3 16=RHS+3 16

p - 3 16 + 3 16 = - 2 12 + 3 16

AddTerms

Add terms

p = - 2 12 + 3 16

▼

Simplify right-hand side

WriteSum

Write as a sum

p = - (2 + 1/2) + 3 + 1/6

Distr

Distribute - 1

p = - 2 - 1/2 + 3 + 1/6

CommutativePropAdd

Commutative Property of Addition

p = - 2 + 3 - 1/2 + 1/6

ExpandFrac

a/b=a * 3/b * 3

p = - 2 + 3 - 36 + 16

AddTerms

Add terms

p = 1 - 2/6

ReduceFrac

a/b=.a /2./.b /2.

p = 1 - 1/3

SubTerm

Subtract term

p = 2/3

To check that this solution is correct, let's substitute p = 23 into the original equation and simplify.

p - 3 16 = - 2 12

Substitute

p= 2/3

2/3 - 3 16 ? =- 2 12

ExpandFrac

a/b=a * 2/b * 2

4/6 - 3 16 ? =- 2 12

WriteDiff

Write as a difference

46 - 3 - 16 ? =- 2 12

SubTerm

Subtract term

3/6 - 3 ? =- 2 12

ReduceFrac

a/b=.a /3./.b /3.

1/2 - 3 ? =- 2 12

SubTerm

Subtract term

- 2 12 = - 2 12 ✓

Since the left-hand side and right-hand side are equal, p = 23 is the correct solution.