Question
Solve for x . 4x=−24 (1 point) explain the correct answer
Answers
Answer
so lets say I had -16x and -78 would I go with negative 6 or regular 6, explain
Answer
my bad I actually meant 13x or 13
Answer
no, this is meant for the 2nd question I asked, i messed up saying 6- and 6, I meant to say 13 and 13-
Answered by
GPT-4o mini
To solve the equation \( 4x = -24 \), follow these steps:
1. **Isolate \( x \)**: To do this, divide both sides of the equation by 4.
\[
x = \frac{-24}{4}
\]
2. **Simplify the right side**:
\[
x = -6
\]
So, the solution to the equation \( 4x = -24 \) is \( x = -6 \).
### Explanation of the Correct Answer
- The equation \( 4x = -24 \) indicates that 4 times some number \( x \) equals -24.
- To find \( x \), we need to determine what number \( x \) would require multiplying by 4 to get -24.
- Dividing both sides of the equation by 4 effectively undoes the multiplication, isolating \( x \) on one side of the equation.
- The division yields \( x = -6 \), which means that if we substitute \( -6 \) back into the original equation, \( 4 \times (-6) = -24 \), confirming that our solution is indeed correct.
1. **Isolate \( x \)**: To do this, divide both sides of the equation by 4.
\[
x = \frac{-24}{4}
\]
2. **Simplify the right side**:
\[
x = -6
\]
So, the solution to the equation \( 4x = -24 \) is \( x = -6 \).
### Explanation of the Correct Answer
- The equation \( 4x = -24 \) indicates that 4 times some number \( x \) equals -24.
- To find \( x \), we need to determine what number \( x \) would require multiplying by 4 to get -24.
- Dividing both sides of the equation by 4 effectively undoes the multiplication, isolating \( x \) on one side of the equation.
- The division yields \( x = -6 \), which means that if we substitute \( -6 \) back into the original equation, \( 4 \times (-6) = -24 \), confirming that our solution is indeed correct.
Answered by
GPT-4o mini
If you're asking about solving an equation like \(-16x = -78\), let's go through the steps and see how the negative signs affect the solution.
1. **Set up the equation**:
\[
-16x = -78
\]
2. **Isolate \( x \)**: To do this, divide both sides of the equation by \(-16\).
\[
x = \frac{-78}{-16}
\]
3. **Simplify the right side**:
Since dividing two negative numbers gives a positive result:
\[
x = \frac{78}{16}
\]
4. **Simplify the fraction**: You can reduce \( \frac{78}{16} \).
- Both 78 and 16 can be divided by 2:
\[
x = \frac{39}{8}
\]
### Explanation of the Result
In the context of your question, when you have \(-16x\) and \(-78\):
- The negative signs cancel out when you divide both sides by \(-16\), meaning you'll end up with a positive value for \( x \).
- Therefore, the solution \( x = \frac{39}{8} \) is positive.
Regarding your reference to "negative 6 or regular 6," this does not apply directly in this instance, since \( x\) in \( -16x = -78\) resolves to a positive fraction, as demonstrated.
To summarize: in the case with \(-16x\) and \(-78\), you would end up with a positive value for \( x \), specifically \( x = \frac{39}{8} \).
1. **Set up the equation**:
\[
-16x = -78
\]
2. **Isolate \( x \)**: To do this, divide both sides of the equation by \(-16\).
\[
x = \frac{-78}{-16}
\]
3. **Simplify the right side**:
Since dividing two negative numbers gives a positive result:
\[
x = \frac{78}{16}
\]
4. **Simplify the fraction**: You can reduce \( \frac{78}{16} \).
- Both 78 and 16 can be divided by 2:
\[
x = \frac{39}{8}
\]
### Explanation of the Result
In the context of your question, when you have \(-16x\) and \(-78\):
- The negative signs cancel out when you divide both sides by \(-16\), meaning you'll end up with a positive value for \( x \).
- Therefore, the solution \( x = \frac{39}{8} \) is positive.
Regarding your reference to "negative 6 or regular 6," this does not apply directly in this instance, since \( x\) in \( -16x = -78\) resolves to a positive fraction, as demonstrated.
To summarize: in the case with \(-16x\) and \(-78\), you would end up with a positive value for \( x \), specifically \( x = \frac{39}{8} \).
Answered by
GPT-4o mini
No problem! Let's solve the equation \( 13x = 13 \) step by step.
1. **Set up the equation**:
\[
13x = 13
\]
2. **Isolate \( x \)**: To do this, divide both sides of the equation by 13.
\[
x = \frac{13}{13}
\]
3. **Simplify the right side**:
\[
x = 1
\]
### Explanation of the Result
In this case, you had \( 13x = 13 \), which means that \( 13\) times some number \( x \) equals \( 13\).
- By dividing both sides by \( 13\), you determine that \( x\) must equal \( 1\).
- This makes sense because multiplying \( 13\) by \( 1\) gives \( 13\).
### Conclusion
Thus, the correct answer is \( x = 1\). This means in the context of your question, if you were wondering whether \( x\) would be negative or positive, it is simply \( 1\) (positive) in this case.
1. **Set up the equation**:
\[
13x = 13
\]
2. **Isolate \( x \)**: To do this, divide both sides of the equation by 13.
\[
x = \frac{13}{13}
\]
3. **Simplify the right side**:
\[
x = 1
\]
### Explanation of the Result
In this case, you had \( 13x = 13 \), which means that \( 13\) times some number \( x \) equals \( 13\).
- By dividing both sides by \( 13\), you determine that \( x\) must equal \( 1\).
- This makes sense because multiplying \( 13\) by \( 1\) gives \( 13\).
### Conclusion
Thus, the correct answer is \( x = 1\). This means in the context of your question, if you were wondering whether \( x\) would be negative or positive, it is simply \( 1\) (positive) in this case.
Answered by
GPT-4o mini
Got it! Let’s clarify your original question in the context of the equation \( -16x = -78\) and how it compares to \( 13x = 13\) or some form of it.
### Let's use the example \( -16x = -78\):
1. **Starting with the equation**:
\[
-16x = -78
\]
2. **Dividing both sides by \(-16\)**:
\[
x = \frac{-78}{-16}
\]
On simplification:
\[
x = \frac{78}{16}
\]
Which further simplifies to:
\[
x = \frac{39}{8} \quad \text{(which is approximately 4.875)}
\]
### Now, for \( 13x = 13\):
1. **Set up the equation**:
\[
13x = 13
\]
2. **Divide both sides by 13**:
\[
x = \frac{13}{13}
\]
3. **Simplify**:
\[
x = 1
\]
### Comparison:
- In the context you were asking about:
- When you have a positive number \( 13x\) (resulting in \( x = 1\)), the output is straightforward and positive.
- When you have a negative coefficient such as \(-16x\) (resulting in \( x = \frac{39}{8}\), which is also positive), the division of negative numbers cancels out the negatives, leading to a positive result.
### Conclusion:
In both cases:
- **For \(13x = 13\)**, the solution is \( x = 1\) (positive).
- **For \( -16x = -78\)**, the solution simplifies to \( x = \frac{39}{8}\) (also positive).
So, regardless of whether you're dividing by a positive or a negative coefficient, if both sides of the equation are negative (as in \(-16x = -78\)), the negatives cancel out, leading to a positive value for \( x\).
Hope this clears it up!
### Let's use the example \( -16x = -78\):
1. **Starting with the equation**:
\[
-16x = -78
\]
2. **Dividing both sides by \(-16\)**:
\[
x = \frac{-78}{-16}
\]
On simplification:
\[
x = \frac{78}{16}
\]
Which further simplifies to:
\[
x = \frac{39}{8} \quad \text{(which is approximately 4.875)}
\]
### Now, for \( 13x = 13\):
1. **Set up the equation**:
\[
13x = 13
\]
2. **Divide both sides by 13**:
\[
x = \frac{13}{13}
\]
3. **Simplify**:
\[
x = 1
\]
### Comparison:
- In the context you were asking about:
- When you have a positive number \( 13x\) (resulting in \( x = 1\)), the output is straightforward and positive.
- When you have a negative coefficient such as \(-16x\) (resulting in \( x = \frac{39}{8}\), which is also positive), the division of negative numbers cancels out the negatives, leading to a positive result.
### Conclusion:
In both cases:
- **For \(13x = 13\)**, the solution is \( x = 1\) (positive).
- **For \( -16x = -78\)**, the solution simplifies to \( x = \frac{39}{8}\) (also positive).
So, regardless of whether you're dividing by a positive or a negative coefficient, if both sides of the equation are negative (as in \(-16x = -78\)), the negatives cancel out, leading to a positive value for \( x\).
Hope this clears it up!