Which of these are solutions to the equation -6(3x + 2) = 2x - 5 - 20x - 7? Select ALL that apply.
Understand the Problem
The question is asking us to determine which of the given values for 'x' satisfy the equation -6(3x + 2) = 2x - 5 - 20x - 7. We need to solve the equation to find all valid solutions and then check each option.
Answer
All of the options: \( x = 6, x = 2, x = 4 \).
Answer for screen readers
The solutions are ( x = 6 ), ( x = 2 ), and ( x = 4 ).
Steps to Solve
- Distribute on the left side of the equation
Start by distributing -6 across the terms inside the parentheses:
$$ -6(3x + 2) = -18x - 12 $$
So the equation becomes:
$$ -18x - 12 = 2x - 5 - 20x - 7 $$
- Combine like terms on the right side
Combine the terms on the right side of the equation:
$$ 2x - 20x = -18x $$
and
$$ -5 - 7 = -12 $$
Therefore, the equation simplifies to:
$$ -18x - 12 = -18x - 12 $$
- Analyze the resulting equation
Both sides of the equation are equal. This means the equation is true for all values of ( x ).
- Check the options provided
Since the equation holds for all ( x ), we check each of the provided options (A, B, C):
- ( x = 6 )
- ( x = 2 )
- ( x = 4 )
All values satisfy the equation.
The solutions are ( x = 6 ), ( x = 2 ), and ( x = 4 ).
More Information
This equation simplifies to the identity ( -18x - 12 = -18x - 12 ), indicating that every value of ( x ) satisfies it. Thus, any value provided in the options will be a solution.
Tips
- Ignoring combinations of terms: Failing to combine like terms properly on the right side can lead to incorrect conclusions about the equality.
- Overcomplicating the analysis: Assuming the equation needs particular values when it’s valid for all real numbers could lead to confusion.
AI-generated content may contain errors. Please verify critical information