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 The equation solved correctly would show that it has
no solution.
In the first step, the student distributed the 4 on the left side of the equation:
4(2-3x) = 8-12x
On the right side, the student distributed the -2 on the term inside the parenthesis, and the -1 on the term outside the parenthesis:
x - 2(2x+1) = x - 4x - 2
Simplifying the equation further, the student collected like terms on both sides:
8 - 12x = -3x - 2
Next, the student attempted to isolate the variable by moving the x terms to the left side and the constant terms to the right side:
8 - 12x + 3x = -2
However, the student made a mistake at this step. It should have been:
8 - 12x + 3x = -2
Combining like terms, the student simplified the equation to:
8 - 9x = -2
At this point, the student tried to isolate the variable by moving the constant terms to the left side and the x term to the right side:
-9x = -10
Finally, the student divided both sides of the equation by -9 to solve for x:
x = 10/9
This is where the student made a mistake. When dividing both sides by -9, the coefficients and the constant on both sides of the equation cancel out:
x = 10/9
Since there are no variables left on the right side of the equation, it means there is no solution.
So, the student's work correctly shows that the equation has no solution.