Question

To rewrite the equation \( \frac{4x}{3x - 12} + 3 = 10 \) in two separate equations joined by "and," we can first isolate the fraction:
1. Start with the original equation:
\[
\frac{4x}{3x - 12} + 3 = 10
\]

2. Subtract 3 from both sides:
\[
\frac{4x}{3x - 12} = 10 - 3
\]
\[
\frac{4x}{3x - 12} = 7
\]

Now, we can separate these into two equations:

1. The first equation represents the fraction:
\[
\frac{4x}{3x - 12} = 7
\]

2. 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:
\[
\frac{4x}{3x - 12} = 7 \quad \text{and} \quad 3 = 3
\]
make tis alot smaller

Answer 1

To rewrite the equation \( \frac{4x}{3x - 12} + 3 = 10 \) in a more concise form, we can follow these steps:

1. Start with the original equation:
\[
\frac{4x}{3x - 12} + 3 = 10
\]

2. Subtract 3 from both sides:
\[
\frac{4x}{3x - 12} = 7
\]

Now, we can express this as two separate equations:

1. The first equation is:
\[
\frac{4x}{3x - 12} = 7
\]

2. The second equation can be simplified to:
\[
3 = 3
\]

Therefore, the final concise version, focusing on the meaningful part, is:
\[
\frac{4x}{3x - 12} = 7 \quad \text{and} \quad 10 - 3 = 7
\]

Alternatively, if you want to keep it simpler:
\[
\frac{4x}{3x - 12} = 7 \quad \text{and} \quad 3 = 3
\]

However, since \(3 = 3\) is always true, you can just focus on the significant equation.