Examine the solution to the equation.

Question

–6(x + 5) + 3 = –2(x + 4) – 4x

–6x – 30 + 3 = –2x – 8 – 4x

–6x – 27 = –6x – 8

–27 = – 8

Which statements accurately describe this equation? Check all that apply.
This equation has one solution.
This equation has no solution.
This equation has infinitely many solutions.
Any input value for the variable will generate a true equation.
Any input value for the variable will generate a false equation.

Answer 1

Let's analyze the steps leading to the conclusion that was reached in the solution process:

1. The original equation is: \[ -6(x + 5) + 3 = -2(x + 4) - 4x \]

2. The equation is simplified, resulting in: \[ -6x - 30 + 3 = -2x - 8 - 4x \] This simplifies to: \[ -6x - 27 = -6x - 8 \]

3. When we reach the equation: \[ -27 = -8 \] This statement is clearly false.

Since the equation leads to a false statement, it indicates that there is no solution. Therefore, we can evaluate the statements provided:

• This equation has one solution. (False)
• This equation has no solution. (True)
• This equation has infinitely many solutions. (False)
• Any input value for the variable will generate a true equation. (False)
• Any input value for the variable will generate a false equation. (True)

Correct Statements:

• This equation has no solution.
• Any input value for the variable will generate a false equation.