Exercise 1 Page 327

We have been given a partially completed two-column proof. Consider the given statement and the desired result.

• Given: 3(x-4)=2x+7
• Prove: x=19

In order to complete the table, and prove that x=19, we will solve the equation.

Blank b.

Let's start!

We began by distributing 3, which can be justified by the Distributive Property. & b. 3x-12=2x+7 & b. Distributive Property

Blank c.

We will continue with the next step of the proof. We are already told that we need to use Subtraction Property.

We subtracted 2x from both sides of the equation. Therefore, we are ready to fill in the blank space in the Statements column. & c. x-12=7 & c. Subtraction Property

Blank d.

Next, we will complete the last step of the proof.

Since we added 12 to both sides of the equation, the property that justifies this step is the Addition Property. & d. x=19 & d. Addition Property

Completed Proof

Finally, we can view the completed proof table.