Answered

Discover the answers to your questions at Westonci.ca, where experts share their knowledge and insights with you. Connect with a community of professionals ready to help you find accurate solutions to your questions quickly and efficiently. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts.

Write a justification for each step. Choose from the following reasons:

- Addition Property of Equality
- Segment Addition Postulate
- Substitution Property of Equality
- Division Property of Equality
- Simplify
- Subtraction Property of Equality

Given:
[tex]\[ HJ = HI + IJ \][/tex]
[tex]\[ 7x - 3 = (2x + 6) + (3x - 3) \][/tex]

Steps:
1. [tex]\( 7x - 3 = 5x + 3 \)[/tex] (Simplify)
2. [tex]\( 7x - 5x - 3 = 3 \)[/tex] (Subtraction Property of Equality)
3. [tex]\( 2x - 3 = 3 \)[/tex] (Simplify)
4. [tex]\( 2x - 3 + 3 = 3 + 3 \)[/tex] (Addition Property of Equality)
5. [tex]\( 2x = 6 \)[/tex] (Simplify)
6. [tex]\( x = 3 \)[/tex] (Division Property of Equality)

Sagot :

GinnyAnswer
Certainly! Here is the detailed step-by-step solution along with the justifications for each step:

1. Apply the Segment Addition Postulate:
- Original Equation: [tex]\( 7x - 3 = (2x + 6) + (3x - 3) \)[/tex]
- Justification: Segment Addition Postulate

2. Simplify the right side:
- Simplified Equation: [tex]\( 7x - 3 = 5x + 3 \)[/tex]
- Justification: Simplify

3. Subtract [tex]\( 5x \)[/tex] from both sides:
- Equation after Subtraction: [tex]\( 7x - 5x - 3 = 5x - 5x + 3 \)[/tex]
- Simplified: [tex]\( 2x - 3 = 3 \)[/tex]
- Justification: Subtraction Property of Equality

4.Add 3 to both sides:
- Equation after Addition: [tex]\( 2x - 3 + 3 = 3 + 3 \)[/tex]
- Simplified: [tex]\( 2x = 6 \)[/tex]
- Justification: Addition Property of Equality

5. Divide both sides by 2:
- Equation after Division: [tex]\( 2x / 2 = 6 / 2 \)[/tex]
- Simplified: [tex]\( x = 3 \)[/tex]
- Justification: Division Property of Equality

Summary of steps with justifications:
1. [tex]\( 7x - 3 = (2x + 6) + (3x - 3) \)[/tex]
- Segment Addition Postulate
2. [tex]\( 7x - 3 = 5x + 3 \)[/tex]
- Simplify
3. [tex]\( 2x - 3 = 3 \)[/tex]
- Subtraction Property of Equality
4. [tex]\( 2x = 6 \)[/tex]
- Addition Property of Equality
5. [tex]\( x = 3 \)[/tex]
- Division Property of Equality
Thank you for your visit. We're dedicated to helping you find the information you need, whenever you need it. Your visit means a lot to us. Don't hesitate to return for more reliable answers to any questions you may have. Get the answers you need at Westonci.ca. Stay informed by returning for our latest expert advice.