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
based on the students work the equation was solved _
the equation solved correctly would show that is has _ solution
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 using the Distributive Property to simplify both sides of the equation.
The equation solved correctly would show that it has no solution.
Based on the student's work, the equation was solved using the properties of algebraic equations. However, there seems to be an error in their solution, which leads to the conclusion that the equation has no solution.
To solve the equation correctly, let's go through the steps:
Step 1: Distribute the 4 on the left side and the -2 on the right side:
4 * 2 - 4 * 3x = x - 2 * 2x - 2 * 1
8 - 12x = x - 4x - 2
Step 2: Combine like terms on both sides of the equation:
-12x + 8 = x - 4x - 2
-12x + 8 = -3x - 2
At this point, the equation should be:
-12x + 8 = -3x - 2
However, the student made an error in their work:
8 - 3x = -3x - 2
They mistakenly dropped the x term on the right side of the equation. Therefore, the student's work is incorrect.
To solve the equation correctly, let's continue:
Step 3: Get rid of the x term on the right side by adding 3x to both sides:
8 - 3x + 3x = -3x + 3x - 2
8 = -2
Step 4: Simplify the equation:
8 = -2
At this point, we have an illogical statement. The equation is saying that 8 is equal to -2, which is not true. Therefore, the equation has no solution.
So, based on the student's work, the equation was solved incorrectly, and the correct solution shows that it has no solution.