Question

Question
Look at the steps for solving the equation and choose a true statement.

3x−9x+1=2(−3x+1)−1
3
𝑥
−
9
𝑥
+
1
=
2
(
−
3
𝑥
+
1
)
−
1


−6x+1=−6x+2−1
−
6
𝑥
+
1
=
−
6
𝑥
+
2
−
1


−6x+1=−6x+1
−
6
𝑥
+
1
=
−
6
𝑥
+
1


(1 point)
Responses

There are infinitely many solutions to the equation.
There are infinitely many solutions to the equation.

There are no solutions to the equation.
There are no solutions to the equation.

The only solution to the equation is –6.
The only solution to the equation is –6.

The only solution to the equation is 1.
The only solution to the equation is 1.

There is no way to know if there is a solution to this equation.

Answer 1

Infinitely many solutions. After simplifying both sides you get

3x − 9x + 1 = −6x + 1
2(−3x + 1) − 1 = −6x + 2 − 1 = −6x + 1,

so the equation becomes −6x + 1 = −6x + 1, which is true for every x.