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 correct solution involves simplifying the equation and isolating the variable on one side.
Let's solve the equation step-by-step:
1. Distribute the 4 on the left side:
4 * 2 - 4 * 3x = x - 2(2x + 1)
8 - 12x = x - 4x - 2
2. Simplify the equation:
8 - 12x = x - 4x - 2
3. Combine like terms on the right side:
8 - 12x = -3x - 2
4. Move all the x-terms to one side:
8 - 12x + 3x = -2
Simplifying:
8 - 9x = -2
5. Move the constant term to the right side:
8 - 9x + 2 = 0
Simplifying:
10 - 9x = 0
6. Move the constant term to the left side:
10 - 9x - 10 = 0 - 10
Simplifying:
- 9x = -10
7. Divide both sides by -9 to solve for x:
(-9x) / -9 = (-10) / -9
Simplifying:
x = 10/9
Therefore, the correct solution to the equation is x = 10/9, indicating that there is one solution.