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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 :

GinnyAnsweridn
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
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