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Elementary Geometry for College St...

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

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BuyFindarrow_forward

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: 3 ( x 5 ) = 21
Prove: x = 12
PROOF
Statements Reasons
1. 3 ( x 5 ) = 21 1. ?
2. 3 x 15 = 21 2. ?
3. 3 x = 36 3. ?
4. x = 12 4. ?

To determine

To find:

The missing reasons for the algebraic proof.

Explanation

Given:

The given table is shown below.

PROOF
Statements Reasons
1. 3(x5)=21 1. ?
2. 3x15=21 2. ?
3. 3x=36 3. ?
4. x=12 4. ?

Approach:

1. The Distributive Property of Equality is,

a(b+c)=ab+ac

2. The Additive Property of Equality states that if same number is added to both sides of the equation then the sides of the equation remains equal.

3. The Division Property of Equality states that if both sides of an equation are 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.

3(x5)=21

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.

3(x5)=21

Rewrite the difference inside the parenthesis as a sum.

3(x+(5))=21

Use Distributive Property of Equality.

3x+3(5)=213x15=21

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

Now go from the second statement to third statement.

3x15=21

Use Addition Property of Equality and add 15 to both sides of the above equation

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