First, state the given information. Then, solve the equation and justify each step.
Statements
Reasons
1.
- 3r+1/2=4
1.
Given
2.
- 3r+1/2-1/2=4-1/2
2.
Subtraction Property of Equality
3.
-3r=7/2
3.
Substitution Property of Equality
4.
-1/3(-3r)=-1/3(7/2)
4.
Multiplication Property of Equality
5.
r=-7/6
5.
Substitution Property of Equality
Practice makes perfect
For the given conjecture, we will write a two-column proof.
If - 3r+1/2=4, then r=-7/6.
Remember that in a proof, we first state the given information.
Given
- 3r+1/2=4
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 subtract 12 from both sides of the equation. To do that, we will use the Subtraction Property of Equality.
Subtraction Property of Equality
- 3r+1/2- 1/2=4- 1/2
Next, we will subtract the terms. Using the Substitution Property of Equality, we will rewrite - 3r+1/2- 1/2 and 4- 12 as - 3r and 72, respectively.
Substitution Property of Equality
-3r= 7/2
Now, we can multiply the equation by - 13 by using the Multiplication Property of Equality.
Multiplication Property of Equality
-1/3(-3r)= -1/3(7/2)
In our last step, we will again use the Substitution Property of Equality.
Substitution Property of Equality
r= - 7/6
Combining all of these steps, we can form our two-proof column.
