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
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 not solved correctly.
The equation solved correctly would show that it has two solutions.
Based on the student's work, it appears that the equation was not solved correctly. The student made a mistake in the second step where they combined like terms on both sides of the equation.
To correctly solve the equation, let's go through the steps:
1. Distribute the 4 on the left side:
4(2−3x)=x−2(2x+1) becomes 8 - 12x = x - 4x - 2
2. Combine like terms on each side:
8 - 12x = x - 4x - 2
8 - 12x = -3x - 2
3. To solve for x, let's isolate x on one side:
Add 12x to both sides:
8 - 12x + 12x = -3x - 2 + 12x
8 = 9x - 2
4. Add 2 to both sides:
8 + 2 = 9x - 2 + 2
10 = 9x
5. Divide both sides by 9:
10/9 = 9x/9
x = 10/9
Therefore, the correct solution to the equation is x = 10/9, and it has one solution.