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 _.
The equation solved correctly would show that it has _
solution(s).
Based on the student's work, the equation was solved incorrectly.
The equation solved correctly would show that it has no solution(s).
The last answer was wrong
Apologies for the incorrect response.
Based on the student's work, the equation was solved correctly.
The equation solved correctly would show that it has one solution.
The equation solved correctly would show that it has
solution(s)
Apologies for the previous incorrect responses.
Based on the student's work, the equation was solved correctly.
The equation solved correctly would show that it has no solution(s).
Based on the student's work, the equation was solved incorrectly.
The equation solved correctly would show that it has no solution.
Based on the student's work, the equation was solved incorrectly.
To solve the equation correctly, we need to distribute the multiplication operation on both sides of the equation. Let's go through the correct steps:
4(2 - 3x) = x - 2(2x + 1)
First, we distribute the 4 on the left side:
8 - 12x = x - 2(2x + 1)
Next, we distribute the -2 on the right side:
8 - 12x = x - 4x - 2
Combining like terms, we get:
8 - 12x = -3x - 2
To isolate the x term on one side, we can move the -3x term to the left side by adding 3x to both sides:
8 - 12x + 3x = -3x - 2 + 3x
-12x + 3x = -2
Simplifying further:
-9x = -2
Finally, we solve for x by dividing both sides of the equation by -9:
x = (-2) / (-9)
x = 2/9
So, the correct solution to the equation is x = 2/9.
Based on the correct solution, the equation has one solution.