Which of these are solutions to the equation −6(3x + 2) = 2x − 5 − 20x − 7? Select ALL that apply.
Understand the Problem
The question asks which values of x (among given options) solve the equation −6(3x + 2) = 2x − 5 − 20x − 7. To solve it, we would need to simplify the equation and check each option for validity.
Answer
All values of $x$ satisfy the equation: $x = 6$, $x = 2$, $x = 4$.
Answer for screen readers
All options are solutions: $x = 6$, $x = 2$, and $x = 4$.
Steps to Solve
- Expand both sides of the equation
First, expand the left side and combine like terms on the right side.
For the left side: $$ -6(3x + 2) = -18x - 12 $$
For the right side: $$ 2x - 5 - 20x - 7 = -18x - 12 $$
Now the equation looks like: $$ -18x - 12 = -18x - 12 $$
- Analyze the simplified equation
Notice that the left side equals the right side, which means the equation holds true for all values of $x$.
- Check the options provided
Since the equation is true for all values:
- Option A: $x = 6$
- Option B: $x = 2$
- Option C: $x = 4$
All these values satisfy the original equation.
All options are solutions: $x = 6$, $x = 2$, and $x = 4$.
More Information
The equation simplifies to a true statement, meaning every possible value of $x$ satisfies it. This type of equation is called an identity.
Tips
- Neglecting to simplify: Some may skip simplifying the equation completely, missing that it holds for all $x$.
- Assuming only specific values can be solutions: When an equation simplifies to a true statement, all values are valid solutions.
AI-generated content may contain errors. Please verify critical information
