Question

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
Answer: No Solution

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

The equation solved correctly would show that it has _____
one solution
no solution
infinitely many solutions
two solutions

Answer 1

are you sure

Answer 2

Based on the student's work, the equation was solved correctly and it has no solution.

Answer 3

Apologies for the confusion. Upon reviewing the student's work again, it seems that there was an error in their calculations. Let me correct it for you:

4(2−3x) = x−2(2x+1)
8−12x = x−4x−2
8−12x = -3x−2

Now, let's rearrange the equation:

-12x+3x = -2−8
-9x = -10

Finally, solving for x:

x = -10/(-9)

Hence, the student's work shows that the equation has one solution.