Solve For $y$. ∣ Y ∣ = 6 |y| = 6 ∣ Y ∣ = 6 If There Is More Than One Solution, Separate Them With Commas. If There Is No Solution, Click On No Solution. Y = Y = Y =
Understanding the Absolute Value Equation
When dealing with absolute value equations, we need to consider both the positive and negative possibilities of the variable. In this case, we have the equation |y| = 6, which means that the absolute value of y is equal to 6.
Breaking Down the Absolute Value Equation
To solve the absolute value equation |y| = 6, we need to consider two cases:
- Case 1: y is positive
- Case 2: y is negative
Case 1: y is positive
If y is positive, then the absolute value of y is equal to y itself. So, we can write the equation as y = 6. This means that y is equal to 6.
Case 2: y is negative
If y is negative, then the absolute value of y is equal to the negative of y. So, we can write the equation as -y = 6. To solve for y, we need to multiply both sides of the equation by -1, which gives us y = -6.
Combining the Solutions
Now that we have considered both cases, we can combine the solutions to get the final answer. In this case, we have two possible solutions: y = 6 and y = -6.
Conclusion
In conclusion, the solution to the absolute value equation |y| = 6 is y = 6, y = -6. This means that y can be either 6 or -6.
Final Answer
The final answer is:
Understanding the Absolute Value Equation
When dealing with absolute value equations, we need to consider both the positive and negative possibilities of the variable. In this case, we have the equation |y| = 6, which means that the absolute value of y is equal to 6.
Q&A: Solving Absolute Value Equations
Q: What is the absolute value of a number?
A: The absolute value of a number is its distance from zero on the number line. It is always non-negative.
Q: How do I solve an absolute value equation?
A: To solve an absolute value equation, you need to consider two cases:
- Case 1: The variable is positive
- Case 2: The variable is negative
Q: What is the solution to the equation |y| = 6?
A: The solution to the equation |y| = 6 is y = 6 and y = -6.
Q: Why do I need to consider both positive and negative cases?
A: You need to consider both positive and negative cases because the absolute value of a number can be either positive or negative. For example, the absolute value of -3 is 3, and the absolute value of 3 is also 3.
Q: Can I have more than one solution to an absolute value equation?
A: Yes, you can have more than one solution to an absolute value equation. In this case, we have two possible solutions: y = 6 and y = -6.
Q: What if I have no solution to an absolute value equation?
A: If you have no solution to an absolute value equation, it means that the equation is not true for any value of the variable. For example, the equation |y| = -6 has no solution because the absolute value of a number is always non-negative.
Common Mistakes to Avoid
Mistake 1: Not considering both positive and negative cases
When solving an absolute value equation, it's essential to consider both positive and negative cases. Failing to do so can lead to incorrect solutions.
Mistake 2: Not checking for extraneous solutions
When solving an absolute value equation, you need to check for extraneous solutions. An extraneous solution is a solution that is not valid for the original equation.
Tips and Tricks
Tip 1: Use a number line to visualize the absolute value equation
Using a number line can help you visualize the absolute value equation and make it easier to solve.
Tip 2: Check for extraneous solutions
When solving an absolute value equation, it's essential to check for extraneous solutions. An extraneous solution is a solution that is not valid for the original equation.
Conclusion
In conclusion, solving absolute value equations requires considering both positive and negative cases. By following the steps outlined in this article, you can solve absolute value equations with confidence.
Final Answer
The final answer is: