Question

A conjecture and a portion of the flowchart proof used to prove the conjecture are shown.

Which equation best represents the information that should be in the box labeled 1?

3x = 9

3x = 26

3x = 27

3x = 30

Answer 1

3x - 1 = 26

addition property of equality, means add 1 to both sides
so 3x = 27

answer
3x = 27 (C. third choice)

Answer 2

The correct option is 3.

Explanation:

Given:
`\overline {PQ}\cong \overline{QR}`,
`PQ=3x-1,QR=26`.

Prove:
`x=9`

`\overline {PQ}\cong \overline{QR}` (Given)

`PQ=QR` (Segment congruent postulate)

`3x-1=26` (Substitution property of equality)

Add 1 on both sides.

`3x-1+1=26+1` (Addition property of equality)

`3x=27`

Divide both sides by 3.

`x=9` (Division property of equality)

Hence proved.

The required equation for box 1 is 3x=27.

Therefore the correct option is 3.