To rewrite the equation \( \frac{4x}{3x - 12} + 3 = 10 \) as two equations joined by "and," we first isolate the fraction on one side:
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Start with the original equation: \[ \frac{4x}{3x - 12} + 3 = 10 \]
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Subtract 3 from both sides: \[ \frac{4x}{3x - 12} = 7 \]
Now we can write it in the form of two equations joined by "and":
\[ \frac{4x}{3x - 12} = 7 \quad \text{and} \quad 3x - 12 \neq 0 \]
The second equation \( 3x - 12 \neq 0 \) is included to ensure that the denominator is not zero.
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