Question

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

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

A. The only solution to the equation is 1

B. There are no solutions to the equation.

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

D. There are infinitely many solutions to the equation.

E. The only solution to the equation is -6

Answer 1

The true statement is:

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

Answer 2

A student solved the following equation using the following steps:

4(2−3x)=x−2(2x+1)
8−3x=x−4x−2
8−3x=−3x−2
No solution.

(2 points)
Based on the student's work, the equation was solved __________

incorrectly or correct

Answer 3

Based on the student's work, the equation was solved correctly.

Answer 4

The equation solved correctly would show that it has _________ solution(s).


A. infinitely many
B. one
C. three
D. two

Answer 5

The equation solved correctly would show that it has:

B. one solution

Answer 6

A student solved the following equation using the following steps:

2(2x+2)=4(x+4)
4x+4=4x+4
4=4
Infinitely many solutions

(2 points)
Based on the student's work, the equation was solved _______

The equation solved correctly would show that it has ________ solution(s).

Answer 7

Based on the student's work, the equation was solved correctly.

The equation solved correctly would show that it has:

D. infinitely many solutions

Answer 8

2(2x+2)=4(x+4)

Answer 9

Let's look at the steps given by the student:

2(2x+2)=4(x+4)
4x+4=4x+16
4x-4x=16-4
0=12

Based on the student's work, the equation was solved incorrectly.

The correct solution to the equation 2(2x+2)=4(x+4) is as follows:

2(2x+2)=4(x+4)
4x+4=4x+16
4x+4x=16
8x=16
x=2

So, the equation has B. one solution.