What Is The Solution To $3|-3x + 9| = -18$?A. $x = -5$ B. $ X = 5 X = 5 X = 5 $ Or X = 1 X = 1 X = 1 $ C. $ X = − 5 X = -5 X = − 5 $ Or X = 1 X = 1 X = 1 $ D. No Solution
Introduction
When dealing with absolute value equations, it's essential to consider the two possible cases: when the expression inside the absolute value is positive and when it's negative. In this article, we'll explore the solution to the equation $3|-3x + 9| = -18$ and determine the correct answer among the given options.
Understanding Absolute Value Equations
Absolute value equations involve expressions inside absolute value symbols, denoted by vertical lines. The absolute value of a number is its distance from zero on the number line, without considering direction. When solving absolute value equations, we need to consider two cases:
- When the expression inside the absolute value is positive
- When the expression inside the absolute value is negative
Case 1: When the Expression Inside the Absolute Value is Positive
In this case, we can remove the absolute value symbol and solve the resulting equation. The equation becomes:
To solve for x, we can start by dividing both sides of the equation by 3:
Next, we can subtract 9 from both sides of the equation:
Finally, we can divide both sides of the equation by -3 to solve for x:
Case 2: When the Expression Inside the Absolute Value is Negative
In this case, we can remove the absolute value symbol and change the sign of the expression inside the absolute value. The equation becomes:
Simplifying the equation, we get:
To solve for x, we can start by dividing both sides of the equation by 3:
Next, we can add 9 to both sides of the equation:
Finally, we can divide both sides of the equation by 3 to solve for x:
Conclusion
In conclusion, we have found two possible solutions to the equation $3|-3x + 9| = -18$: and . Therefore, the correct answer among the given options is:
B. or
Final Answer
The final answer is B.
Introduction
In the previous article, we explored the solution to the equation $3|-3x + 9| = -18$. In this article, we'll address some frequently asked questions (FAQs) about absolute value equations.
Q: What is an absolute value equation?
A: An absolute value equation is an equation that involves an expression inside absolute value symbols, denoted by vertical lines. The absolute value of a number is its distance from zero on the number line, without considering direction.
Q: How do I solve an absolute value equation?
A: To solve an absolute value equation, you need to consider two cases:
- When the expression inside the absolute value is positive
- When the expression inside the absolute value is negative
Q: What is the difference between the two cases?
A: In the first case, you can remove the absolute value symbol and solve the resulting equation. In the second case, you can remove the absolute value symbol and change the sign of the expression inside the absolute value.
Q: Can I always remove the absolute value symbol and solve the resulting equation?
A: No, you can only remove the absolute value symbol and solve the resulting equation when the expression inside the absolute value is positive. When the expression inside the absolute value is negative, you need to remove the absolute value symbol and change the sign of the expression inside the absolute value.
Q: How do I know which case to use?
A: To determine which case to use, you need to evaluate the expression inside the absolute value. If the expression is positive, use the first case. If the expression is negative, use the second case.
Q: Can I have multiple solutions to an absolute value equation?
A: Yes, you can have multiple solutions to an absolute value equation. This occurs when the expression inside the absolute value is equal to both a positive and a negative value.
Q: How do I check my solutions?
A: To check your solutions, substitute each solution back into the original equation and verify that it is true.
Q: What if I have a quadratic equation inside the absolute value?
A: If you have a quadratic equation inside the absolute value, you can factor the quadratic equation and solve for the values of x that make the quadratic equation equal to both a positive and a negative value.
Q: Can I use absolute value equations to model real-world problems?
A: Yes, absolute value equations can be used to model real-world problems that involve distances, temperatures, and other quantities that can be positive or negative.
Conclusion
In conclusion, absolute value equations can be used to model a wide range of real-world problems. By understanding how to solve absolute value equations, you can develop problem-solving skills that can be applied to various fields, including science, engineering, and economics.
Final Answer
The final answer is that absolute value equations are a powerful tool for modeling and solving real-world problems. By understanding how to solve absolute value equations, you can develop problem-solving skills that can be applied to various fields.