To rewrite the equation \( \frac{4x}{3x - 12} + 3 = 10 \) in two separate equations joined by "and," we can first isolate the fraction:
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Start with the original equation: \[ \frac{4x}{3x - 12} + 3 = 10 \]
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Subtract 3 from both sides: \[ \frac{4x}{3x - 12} = 10 - 3 \] \[ \frac{4x}{3x - 12} = 7 \]
Now, we can separate these into two equations:
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The first equation represents the fraction: \[ \frac{4x}{3x - 12} = 7 \]
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The second equation comes from the manipulation we did: \[ 3 = 10 - 7 \]
Thus, the two equations joined by "and" will be: \[ \frac{4x}{3x - 12} = 7 \quad \text{and} \quad 3 = 3 \]
However, since \(3 = 3\) is always true, we can keep the equation focused on the meaningful part: \[ \frac{4x}{3x - 12} = 7 \quad \text{and} \quad x \in \mathbb{R} \]
If you want to keep it more relevant, you could express the process instead: \[ \frac{4x}{3x - 12} = 7 \quad \text{and} \quad 10 - 3 = 7 \]
But the main equation you seek is: \[ \frac{4x}{3x - 12} = 7 \quad \text{and} \quad 3 = 3 \]
Choose whichever form suits your needs better!