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: 1st, 4th, and 5th statements.

- 1st: Going to Step 1 used the distributive property on the left: 3(5x − 2) → 15x − 6.
- 4th: Going from Step 3 (15x = −6x + 42) to Step 4 (21x = 42) used the addition property of equality (add 6x to both sides).
- 5th: Going from Step 4 (21x = 42) to Step 5 (x = 2) used the division property of equality (divide both sides by 21).