Question
Find the error
x/6+3=-18
3-3 -18-3
6 x x/6=15 x 6
x=-90
x/6+3=-18
3-3 -18-3
6 x x/6=15 x 6
x=-90
Answers
GPT-4o mini
Let's solve the equation step by step and find the error.
The original equation is:
\[
\frac{x}{6} + 3 = -18
\]
1. **Subtract 3 from both sides:**
\[
\frac{x}{6} = -18 - 3
\]
Simplifying this gives:
\[
\frac{x}{6} = -21
\]
2. **Multiply both sides by 6 to solve for \(x\):**
\[
x = -21 \times 6
\]
Calculating the right side:
\[
x = -126
\]
The correct solution is \(x = -126\).
Now looking at the steps you provided:
- The line “3 - 3 - 18 - 3” does not relate to the original equation correctly.
- The line “\(6 \times x/6 = 15 \times 6\)” does not follow from any of the earlier steps.
Thus, the mistake is in these operations and the interpretation of the equation. The correct solution is \(x = -126\), not \(x = -90\).
The original equation is:
\[
\frac{x}{6} + 3 = -18
\]
1. **Subtract 3 from both sides:**
\[
\frac{x}{6} = -18 - 3
\]
Simplifying this gives:
\[
\frac{x}{6} = -21
\]
2. **Multiply both sides by 6 to solve for \(x\):**
\[
x = -21 \times 6
\]
Calculating the right side:
\[
x = -126
\]
The correct solution is \(x = -126\).
Now looking at the steps you provided:
- The line “3 - 3 - 18 - 3” does not relate to the original equation correctly.
- The line “\(6 \times x/6 = 15 \times 6\)” does not follow from any of the earlier steps.
Thus, the mistake is in these operations and the interpretation of the equation. The correct solution is \(x = -126\), not \(x = -90\).
you understand I took 3 out of 3 and began to subtract 18 and 3 yes?
GPT-4o mini
Thank you for clarifying your approach. Let's break down the operation step by step based on your explanation and see where the mistake might have occurred.
Starting with the equation:
\[
\frac{x}{6} + 3 = -18
\]
You mentioned you took 3 out of 3 and began to subtract 18 and 3. If we interpret that correctly, here's how the operations would go:
1. From \(\frac{x}{6} + 3 = -18\), if we correctly subtract 3 from both sides:
\[
\frac{x}{6} = -18 - 3
\]
This simplifies to:
\[
\frac{x}{6} = -21
\]
2. Now, multiplying both sides by 6 gives:
\[
x = -21 \times 6 = -126
\]
It appears you may have been trying to combine or manipulate values in a way that introduced confusion. The correct steps come from very straightforward algebraic manipulation, focusing on isolating \(x\).
### Summary of the Error
- The operation “3 - 3 - 18 - 3” does not correspond correctly to any part of the original equation.
- Your final result of \(x = -90\) does not emerge from the correct algebraic manipulation of the original equation.
Indeed, the correct value for \(x\) as shown is \(-126\). If you have any specific questions on the particular steps you took, feel free to provide them, and we can analyze them further!
Starting with the equation:
\[
\frac{x}{6} + 3 = -18
\]
You mentioned you took 3 out of 3 and began to subtract 18 and 3. If we interpret that correctly, here's how the operations would go:
1. From \(\frac{x}{6} + 3 = -18\), if we correctly subtract 3 from both sides:
\[
\frac{x}{6} = -18 - 3
\]
This simplifies to:
\[
\frac{x}{6} = -21
\]
2. Now, multiplying both sides by 6 gives:
\[
x = -21 \times 6 = -126
\]
It appears you may have been trying to combine or manipulate values in a way that introduced confusion. The correct steps come from very straightforward algebraic manipulation, focusing on isolating \(x\).
### Summary of the Error
- The operation “3 - 3 - 18 - 3” does not correspond correctly to any part of the original equation.
- Your final result of \(x = -90\) does not emerge from the correct algebraic manipulation of the original equation.
Indeed, the correct value for \(x\) as shown is \(-126\). If you have any specific questions on the particular steps you took, feel free to provide them, and we can analyze them further!
and you understand that 18 is negative?
GPT-4o mini
Yes, I understand that \( -18 \) is a negative value. I appreciate your patience as we clarify the problem together. Let's review the equation closely with that in mind.
Starting with the equation:
\[
\frac{x}{6} + 3 = -18
\]
### Steps to Solve
1. **Subtract 3 from both sides:**
\[
\frac{x}{6} = -18 - 3
\]
Since \( -18 \) is indeed negative, we combine the two negative numbers:
\[
\frac{x}{6} = -21
\]
2. **Multiply both sides by 6:**
\[
x = -21 \times 6
\]
Calculating this gives:
\[
x = -126
\]
### Conclusion
Thus, throughout these steps, it's clear that the negative sign associated with 18 leads to consistent algebra, resulting in \( x = -126 \).
Your calculations may have strayed from this correct logical progression, which is likely where the misunderstanding arose leading to the result of \( x = -90 \). If you have more steps you'd like me to evaluate, please share!
Starting with the equation:
\[
\frac{x}{6} + 3 = -18
\]
### Steps to Solve
1. **Subtract 3 from both sides:**
\[
\frac{x}{6} = -18 - 3
\]
Since \( -18 \) is indeed negative, we combine the two negative numbers:
\[
\frac{x}{6} = -21
\]
2. **Multiply both sides by 6:**
\[
x = -21 \times 6
\]
Calculating this gives:
\[
x = -126
\]
### Conclusion
Thus, throughout these steps, it's clear that the negative sign associated with 18 leads to consistent algebra, resulting in \( x = -126 \).
Your calculations may have strayed from this correct logical progression, which is likely where the misunderstanding arose leading to the result of \( x = -90 \). If you have more steps you'd like me to evaluate, please share!
are you allowed to combine -3 + -18, and why?
GPT-4o mini
Yes, you are allowed to combine \(-3\) and \(-18\) because both numbers are negative.
Here's how that works:
### Basic Rules for Combining Negative Numbers
1. **Adding Negative Numbers:** When you add two negative numbers, you essentially move farther away from zero on the number line. For example:
- \(-3 + (-18)\) is the same as \(-3 - 18\), which equals \(-21\).
2. **Combining with the Same Sign:** When combining numbers with the same sign (both negative in this case), you simply add their absolute values and keep the negative sign:
- Absolute values: \(3 + 18 = 21\)
- Since both are negative, the result remains negative: \(-21\).
### Application in Your Equation
In the context of the equation:
\[
\frac{x}{6} + 3 = -18
\]
When you subtract 3 from both sides, you indeed do:
\[
\frac{x}{6} = -18 - 3
\]
This becomes:
\[
\frac{x}{6} = -21
\]
Thus, you correctly combine the two negative numbers to reach \(-21\).
Overall, your manipulation aligns with the rules of arithmetic regarding negative numbers, and you are indeed allowed to combine them. If you have any further questions or need additional clarification, feel free to ask!
Here's how that works:
### Basic Rules for Combining Negative Numbers
1. **Adding Negative Numbers:** When you add two negative numbers, you essentially move farther away from zero on the number line. For example:
- \(-3 + (-18)\) is the same as \(-3 - 18\), which equals \(-21\).
2. **Combining with the Same Sign:** When combining numbers with the same sign (both negative in this case), you simply add their absolute values and keep the negative sign:
- Absolute values: \(3 + 18 = 21\)
- Since both are negative, the result remains negative: \(-21\).
### Application in Your Equation
In the context of the equation:
\[
\frac{x}{6} + 3 = -18
\]
When you subtract 3 from both sides, you indeed do:
\[
\frac{x}{6} = -18 - 3
\]
This becomes:
\[
\frac{x}{6} = -21
\]
Thus, you correctly combine the two negative numbers to reach \(-21\).
Overall, your manipulation aligns with the rules of arithmetic regarding negative numbers, and you are indeed allowed to combine them. If you have any further questions or need additional clarification, feel free to ask!