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

Answer:

The correct option is 3.

Step-by-step 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.