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
7 answers
no solution.
Based on the student’s work, the equation was solved
incorrectly or correctly
The equation solved correctly would show that it has no solution, one solution, infinite solutions, two solutions
incorrectly or correctly
The equation solved correctly would show that it has no solution, one solution, infinite solutions, two solutions
Based on the student's work, the equation was solved correctly.
how did she solved this problem correctly
The student solved the problem correctly by simplifying both sides of the equation and isolating the variable. Here are the steps:
1. Distribute the 4 on the left side: 8 - 12x = x - 2(2x + 1)
2. Simplify the right side: 8 - 12x = x - 4x - 2
3. Combine like terms on the right side: 8 - 12x = -3x - 2
4. Move all terms with x to one side: 8 - 12x + 3x = -2
5. Combine like terms on the left side: -9x + 8 = -2
6. Move the 8 to the right side: -9x = -2 - 8
7. Simplify: -9x = -10
8. Divide both sides by -9: x = -10/-9
9. Simplify: x = 10/9
Since the final value of x is a single number, and not a variable or an expression, the equation has one solution.
1. Distribute the 4 on the left side: 8 - 12x = x - 2(2x + 1)
2. Simplify the right side: 8 - 12x = x - 4x - 2
3. Combine like terms on the right side: 8 - 12x = -3x - 2
4. Move all terms with x to one side: 8 - 12x + 3x = -2
5. Combine like terms on the left side: -9x + 8 = -2
6. Move the 8 to the right side: -9x = -2 - 8
7. Simplify: -9x = -10
8. Divide both sides by -9: x = -10/-9
9. Simplify: x = 10/9
Since the final value of x is a single number, and not a variable or an expression, the equation has one solution.
4(2−3x)=x−2(2x+1)
8−3x=x−4x−2
8−3x=−3x−2
this is how the student did it...so no she did not solve it correctly
8−3x=x−4x−2
8−3x=−3x−2
this is how the student did it...so no she did not solve it correctly
Apologies for the confusion. You are correct. The student did not solve the equation correctly. In the step:
8 - 3x = -3x - 2
The student made an error by subtracting 3x from both sides of the equation. It should be:
8 - 3x = -3x - 2x - 2
Then, simplifying further:
8 - 3x = -5x - 2
The correct steps should be:
1. Distribute the 4 on the left side: 8 - 12x = x - 2(2x + 1)
2. Simplify the right side: 8 - 12x = x - 4x - 2
3. Combine like terms on the right side: 8 - 12x = -3x - 2x - 2
4. Simplify the left side: 8 - 12x = -5x - 2
5. Move all terms with x to one side: 8 - 12x + 5x = -2
6. Combine like terms: -12x + 5x = -2 - 8
7. Simplify: -7x = -10
8. Divide both sides by -7: x = -10 / -7
9. Simplify: x = 10/7
So, the correct answer should be x = 10/7. The equation has one solution, not no solution as originally stated.
8 - 3x = -3x - 2
The student made an error by subtracting 3x from both sides of the equation. It should be:
8 - 3x = -3x - 2x - 2
Then, simplifying further:
8 - 3x = -5x - 2
The correct steps should be:
1. Distribute the 4 on the left side: 8 - 12x = x - 2(2x + 1)
2. Simplify the right side: 8 - 12x = x - 4x - 2
3. Combine like terms on the right side: 8 - 12x = -3x - 2x - 2
4. Simplify the left side: 8 - 12x = -5x - 2
5. Move all terms with x to one side: 8 - 12x + 5x = -2
6. Combine like terms: -12x + 5x = -2 - 8
7. Simplify: -7x = -10
8. Divide both sides by -7: x = -10 / -7
9. Simplify: x = 10/7
So, the correct answer should be x = 10/7. The equation has one solution, not no solution as originally stated.
1 answer