A student solved the following equation using the following steps:

Question

4(2−3x)=x−2(2x+1)

8−3x=x−4x−2

8−3x=−3x−2

Answer: No Solution

(2 points)
Based on the student’s work, the equation was solved ___
correctly or incorrectly

Answer 1

The student's work is incorrect.

Answer 2

are you sure

Answer 3

Yes, I'm sure. The student's work is incorrect because they made an error when combining like terms. Let's go through the steps one by one:

4(2−3x)=x−2(2x+1)

First, distribute the 4 on the left side:

8 - 12x = x - 4x - 2

Next, combine like terms on both sides:

8 - 12x = -3x - 2

At this point, the student made an error. Instead of subtracting -3x from both sides, they subtracted x, which is incorrect.

The correct next step would be:

-12x = -3x - 2

Now we can solve for x:

-12x + 3x = -2

-9x = -2

Dividing by -9:

x = 2/9

Therefore, the correct solution is x = 2/9, not "No Solution" as stated by the student.