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Original Question
Rewrite the equation 4x3x−12+3=10 in two equations joined by “and.”Question
Rewrite the equation 4x/3x−12+3=10 in two equations joined by “and.
Answers
Answered by
GPT-4o mini
To rewrite the equation \( \frac{4x}{3x-12} + 3 = 10 \) in two equations joined by "and," we can first isolate the fraction on one side of the equation.
1. Start with the original equation:
\[
\frac{4x}{3x - 12} + 3 = 10
\]
2. Subtract 3 from both sides:
\[
\frac{4x}{3x - 12} = 10 - 3
\]
This simplifies to:
\[
\frac{4x}{3x - 12} = 7
\]
Now, we can write the equation as two separate equations:
1. The first equation is the isolated fraction:
\[
\frac{4x}{3x - 12} = 7
\]
2. The second equation is the derived part:
\[
3x - 12 \neq 0
\]
So, we can combine these into the final form:
\[
\frac{4x}{3x - 12} = 7 \quad \text{and} \quad 3x - 12 \neq 0
\]
1. Start with the original equation:
\[
\frac{4x}{3x - 12} + 3 = 10
\]
2. Subtract 3 from both sides:
\[
\frac{4x}{3x - 12} = 10 - 3
\]
This simplifies to:
\[
\frac{4x}{3x - 12} = 7
\]
Now, we can write the equation as two separate equations:
1. The first equation is the isolated fraction:
\[
\frac{4x}{3x - 12} = 7
\]
2. The second equation is the derived part:
\[
3x - 12 \neq 0
\]
So, we can combine these into the final form:
\[
\frac{4x}{3x - 12} = 7 \quad \text{and} \quad 3x - 12 \neq 0
\]
Answered by
GPT-4o mini
The equation \( \frac{4x}{3x - 12} + 3 = 10 \) can be rewritten as two separate equations joined by "and" as follows:
\[
\frac{4x}{3x - 12} = 7 \quad \text{and} \quad 3x - 12 \neq 0
\]
This means the first equation is the altered form of the original equation, and the second equation indicates that the denominator cannot be zero.
So your final answer is:
\[
\frac{4x}{3x - 12} = 7 \quad \text{and} \quad 3x - 12 \neq 0
\]
\[
\frac{4x}{3x - 12} = 7 \quad \text{and} \quad 3x - 12 \neq 0
\]
This means the first equation is the altered form of the original equation, and the second equation indicates that the denominator cannot be zero.
So your final answer is:
\[
\frac{4x}{3x - 12} = 7 \quad \text{and} \quad 3x - 12 \neq 0
\]
Answered by
GPT-4o mini
Sure! Here's a simpler breakdown:
1. Start with the original equation:
\[
\frac{4x}{3x - 12} + 3 = 10
\]
2. First, we isolate the fraction:
- Subtract 3 from both sides:
\[
\frac{4x}{3x - 12} = 7
\]
3. The second part ensures that the denominator is not zero:
- The denominator \(3x - 12\) cannot be zero. So we write:
\[
3x - 12 \neq 0
\]
Putting it all together, we have:
\[
\frac{4x}{3x - 12} = 7 \quad \text{and} \quad 3x - 12 \neq 0
\]
This means:
1. \( \frac{4x}{3x - 12} = 7 \) is the main equation.
2. \( 3x - 12 \neq 0 \) makes sure the denominator isn't zero.
That’s the answer in a simplified form!
1. Start with the original equation:
\[
\frac{4x}{3x - 12} + 3 = 10
\]
2. First, we isolate the fraction:
- Subtract 3 from both sides:
\[
\frac{4x}{3x - 12} = 7
\]
3. The second part ensures that the denominator is not zero:
- The denominator \(3x - 12\) cannot be zero. So we write:
\[
3x - 12 \neq 0
\]
Putting it all together, we have:
\[
\frac{4x}{3x - 12} = 7 \quad \text{and} \quad 3x - 12 \neq 0
\]
This means:
1. \( \frac{4x}{3x - 12} = 7 \) is the main equation.
2. \( 3x - 12 \neq 0 \) makes sure the denominator isn't zero.
That’s the answer in a simplified form!
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