First state the given information. Then, solve the equation and justify each step.
Statements
Reasons
1.
- 1/3n=12
1.
Given
2.
-3(- 1/3n)=-3(12)
2.
Multiplication Property of Equality
3.
n=-36
3.
Substitution Property of Equality
Practice makes perfect
For the given conjecture, we will write a two-column proof.
If - 1/3n=12, then n=-36.
Remember that in a proof, we first state the given information.
Given
- 1/3n=12
To continue creating our two-column proof, we will solve the equation and justify each step using the Properties of Equality. The first step we take to isolate x is to multiply the equation by -3. To do that, we will use the Multiplication Property of Equality.
Multiplication Property of Equality
-3(- 1/3n)= -3(12)
Next, we will multiply the terms. Using the Substitution Property of Equality, we will rewrite -3(- 13n) and -3(12) as n and -36, respectively.
Substitution Property of Equality
n= -36
Combining all of these steps, we can form our two-proof column.
