Exercise 32 Page 106

Simplify the equation as much as possible to determine the number of solutions. Use the Distributive Property.

Identity

Practice makes perfect

When identifying the number of solutions there are to an equation, there are three possible outcomes.

Result of Simplifying	Number of Solutions
Variable on one side and constant on the other	One solution
Identity — both sides are identical	All real numbers
Contradiction — both sides are different numbers	No solutions

To find the number of solutions, we will simplify both sides of the given equation as much as possible and observe the result. Let's start by using the Distributive Property.

4-d=-(d-4)

Distr

Distribute -1

4-d=- d-(-4)

SubNeg

a-(- b)=a+b

4-d=- d +4

CommutativePropAdd

Commutative Property of Addition

4-d=4-d

We have identical sides, so our equation is an identity.