You use deductive reasoning when you solve an equation. You can justify each step with a postulate, a property, or a definition. For example, you can use the Distributive Property to justify combining like terms. If you think of the Distributive Property as a b + a c = a ( b + c ) eh b plus eh c equals eh , open b plus , c close  or a b + a c = ( b + c ) a , eh b plus eh c equals , open b plus , c close eh comma  then 2 x + x = ( 2 + 1 ) x = 3 x . 2 x plus . x equals . open 2 plus , 1 close , x equals , 3 x .

Problem 1 Justifying Steps When Solving an Equation

Algebra What is the value of x? Justify each step.

Plan

How can you use the given information?

Use what you know about linear pairs to relate the two angles.

∠ A O M angle eh o m  and ∠ M O C angle m o c  are supplementary.	that form a linear pair are supplementary.
m ∠ A O M + m ∠ M O C = 180 m angle eh o m plus m angle m o c equals 180	Definition of supplementary
( 2 x + 30 ) + x = 180 open 2 x plus . 30 close plus , x equals , 180	Substitution Property
3 x + 30 = 180 3 x plus . 30 equals , 180	Distributive Property
3 x = 150 3 x equals , 150	Subtraction Property of Equality
x = 50 x equals , 50	Division Property of Equality

✓ Got It?

1. What is the value of x? Justify each step.

   Given: A B → eh b vector  bisects ∠ R A N . angle r eh n .

   

Some properties of equality have corresponding properties of congruence.

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