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akposevictor

The justification of each step of the deductive reasoning are:

Step 1: [tex]CD + DE = CE[/tex]

  • Justification: Segment Addition Postulate

Step 2: [tex]8 + (3x + 7) = 6x[/tex]

  • Justification: Substitution

Step 3: [tex]3x + 15 = 6x[/tex]

  • Justification: Combining like terms

Step 4: [tex]15 = 3x[/tex]

  • Justification: Subtraction property of equality

Step 5: [tex]x = 5[/tex]

  • Justification: Division Property of Equality

Step 6: [tex]CE = 6(5)[/tex]

  • Justification: Substitution

Step 1: [tex]CD + DE = CE[/tex]

Justification: Segment Addition Postulate (point D lies in between points C and E)

Step 2: [tex]8 + (3x + 7) = 6x[/tex]

Justification: Substitution (Plug in the value of CD, DE, and CE in the equation).

Step 3: [tex]3x + 15 = 6x[/tex]

Justification: Combining like terms (Add 8 and 7 together).

Step 4: [tex]15 = 3x[/tex]

Justification: Subtraction property of equality (Subtract 3x from both sides of the equation).

Step 5: [tex]x = 5[/tex]

Justification: Division Property of Equality (Divide both sides by 3).

Step 6: [tex]CE = 6(5)[/tex]

Justification: Substitution (Plugging in x = 5 into 6x).

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olayemiolakunle65

The justification of the deductive reasoning requires the qualification of each step in the question with appropriate theorems. The matching of the justification with the deductions are:

From the given diagram, the following are the justifications for the deductive reasoning are appropriate:

Deductive Reasoning                             Justification

1. CD + DE = CE                                     Segment Addition postulate

2. 8 + (3x + 7) = 6x                                 Addition property of equality

3. 3x + 15 = 6x                                       Addition property of equality

4. 15 = 3x                                               Combining like terms

5. x = 5                                                   Division property of equality

6. CE = 6(5)                                             Substitution

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