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

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

1 answer

The student's work is incorrect. If we analyze the steps, we can see where the error occurred.

First, the student distributed the 4 on the left side of the equation correctly:

4(2−3x) = 8 - 12x

Then, the student distributed the -2 on the right side of the equation correctly:

x − 2(2x+1) = x - 4x - 2 = -3x - 2

So far, the student's work is correct, but here is where the error happens:

The student equated the left side and the right side of the equation incorrectly:

8 - 12x = -3x - 2

To solve the equation, we collect like terms:

-12x + 3x = -2 - 8

Simplifying further:

-9x = -10

Finally, we divide both sides of the equation by -9:

x = -10/-9

x = 10/9

Therefore, the equation does have a solution, contrary to what the student concluded.