Question

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.

Answer 1

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

Step-by-step 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..