The following are deductive reasoning for each statement in the algebraic proof given:
1. CD + DE = CE (Segment Addition Postulate)
2. 8 + (3x + 7) = 6x (Substitution)
3. 3x + 15 = 6x (Combining like terms)
4. 15 = 3x (Subtraction Property of Equality)
5. x = 5 (Division Property of Equality)
6. CE = 6(5) (Substitution)
Recall:
- The Segment Addition Postulate states that when a point lies between two endpoints on a line segment, the length of the larger segment equals the sum of the lengths of the two smaller segments formed.
Thus, the following are deductive reasoning for each statement in the algebraic proof given:
1. CD + DE = CE (Segment Addition Postulate)
2. 8 + (3x + 7) = 6x (Substitution)
- Rationale: Plug in the values of CD, DE and CE
3. 3x + 15 = 6x (Combining like terms)
- Rationale: Add 8 and 7 together
4. 15 = 3x (Subtraction Property of Equality)
- Rationale: Subtract 3x from each side of the equation.
5. x = 5 (Division Property of Equality)
- Rationale: Divide each side of the equation by 3).
6. CE = 6(5) (Substitution)
- Rationale: Plugging in the value of x into "6x"
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