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.
Starting with the original equation:
\[ \frac{4x}{3x - 12} + 3 = 10 \]
We can subtract 3 from both sides:
\[ \frac{4x}{3x - 12} = 7 \]
Now we have the two equations:
- \( \frac{4x}{3x - 12} = 7 \)
- \( 3x - 12 \neq 0 \) (to avoid division by zero)
So, we can write:
\[ \frac{4x}{3x - 12} = 7 \quad \text{and} \quad 3x - 12 \neq 0 \]