Question

Vanessa solved the equation
3
(
5
x
−
2
)
=
−
6
(
x
−
6
)
by following the steps shown below.



Step 1:
15
x
−
6
=
−
6
(
x
−
6
)

Step 2:
15
x
−
6
=
−
6
x
+
36

Step 3:
15
x
=
−
6
x
+
42

Step 4:
21
x
=
42

Step 5:
x
=
2



Select THREE statements that correctly justify a step of Vanessa's work.


Vanessa applied the distributive property going from the given equation to step 1.


Vanessa applied the multiplication property of equality going from step 1 to step 2.


Vanessa applied the reflexive property of equality going from step 2 to step 3.


Vanessa applied the addition property of equality going from step 3 to step 4.


Vanessa applied the division property of equality going from step 4 to step 5

Answer 1

Correct choices:

- Vanessa applied the distributive property going from the given equation to step 1.
Reason: 3(5x − 2) → 15x − 6 by distributing 3.

- Vanessa applied the addition property of equality going from step 3 to step 4.
Reason: 15x = −6x + 42 → 21x = 42 by adding 6x to both sides.

- Vanessa applied the division property of equality going from step 4 to step 5.
Reason: 21x = 42 → x = 2 by dividing both sides by 21.