31. algebra fill in the reason that justifies each step.
given: qs = 42
prove: x = 13
reasons
statements
1) qs = 42
2) qr + rs = qs
3) (x + 3) + 2x = 42
4) 3x + 3 = 42
5) 3x = 39
6) x = 13
i a. ?
b. ?
3 c. ?
2 d. ?
5) e. ?
6) f. ?
use the given property to complete the statement.

Step-by-step explanation:

Statements                                        Reasons

1) QS =42                                               Given

2) QR + RS = QS                              Segment Addition Postulate

3) (x + 3) + 2x = 42                            Substitution Property

4) 3x + 3 = 42                                      Simplify

5) 3x = 39                                          Subtraction Property of Equality

6) x=13                                               Division Property of Equality

Explanation:

We have given QS=42. We have to prove that x=13

We will use Segment Addition Postulate which states that given 2 points Q and S, a third point R lies on the line segment QS  if and only if the distances between the points satisfy the equation QR + RS = QS.

Then we will substitute the values in the defined postulate.

where QR= x+3

RS=2x

QS=42

QR+RS=QS

(x+3)+2x= 42

Now simplify the expression by opening the brackets.

x+3+2x=42

3x+3=42

Now subtract 3 from both sides.

3x+3-3=42-3

3x=39

divide both sides by 3.

3x/3 =39/3

x=13..

it is contrapositive

i could not see the question too well so check yourself again too . this is because i want you to get it correct.