   Chapter 1.5, Problem 24E ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

#### Solutions

Chapter
Section ### Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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# In Exercises 23 to 24, fill in the missing reasons for the algebraic proof. Given: 2 x + 9 = 3 Prove: x = − 3 PROOF Statements Reasons 1. 2 x + 9 = 3 1. ? 2. 2 x = − 6 2. ? 3. x = − 3 3. ?

To determine

To find:

The missing reasons for the algebraic proof.

Explanation

Given:

The given table is shown below.

 PROOF Statements Reasons 1. 2x+9=3 1. ? 2. 2x=−6 2. ? 3. x=−3 3. ?

Approach:

1. The Subtraction Property of Equality states that if a number is subtract from one side of an equation then the same number must be subtracted from the other side of equation to maintain the equality of the original equation.

2. The Division Property of Equality states that if both sides of an equation is divided by the same non-zero number then the sides of the equation remains equal.

Calculation:

The first statement of the proof is given below.

2x+9=3

The first statement is same as the given equation. So, the reason for the first statement is given.

Now, go from the first statement to the second statement.

2x+9=3

Use Subtraction Property of Equality and subtract 9 from both side of the equation.

2x+99=392x=6

Therefore, the reason for second statement is Subtraction Property of Equality.

Now go from the second statement to third statement

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