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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

Practice Test

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Exercise 1 Page 327

Solve the equation to determine the steps involved. Then choose the Properties of Equality.

Statements	Reasons
a. 3(x-4)=2x+7	a. Given
b. 3x-12=2x+7	b. Distributive Property
c. x-12=7	c. Subtraction Property
d. x=19	d. Addition Property

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!

3(x-4)=2x+7

Distribute 3

3x-12=2x+7

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.

3x-12=2x+7

LHS- 2x=RHS- 2x

3x- 2x-12=2x - 2x + 7

Subtract terms

x-12=7

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.

x-12=7

LHS+ 12=RHS+ 12

x-12+ 12=7+ 12

Add terms

x=19

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.

Statements	Reasons
a. 3(x-4)=2x+7	a. Given
b. 3x-12=2x+7	b. Distributive Property
c. x-12=7	c. Subtraction Property
d. x=19	d. Addition Property