Question

Rewrite the equation $\frac {4x}{3x-12}+3=10$ in two equations joined by "and."

Answer 1

To rewrite the given equation \(\frac {4x}{3x-12}+3=10\) in two equations joined by "and," we first need to isolate the fraction on one side.

Starting with the equation:

\[
\frac{4x}{3x-12} + 3 = 10
\]

We subtract 3 from both sides:

\[
\frac{4x}{3x-12} = 10 - 3
\]

This simplifies to:

\[
\frac{4x}{3x-12} = 7
\]

Now we can express this in two parts. The first equation is:

\[
\frac{4x}{3x-12} = 7
\]

Next, we will set the equation equal to the numerical result from the right-hand side. The second equation based on our operations is simply:

\[
3x - 12 \neq 0
\]

This is to ensure that the denominator does not become zero. Now, combining these equations with "and," we have:

\[
\frac{4x}{3x-12} = 7 \quad \text{and} \quad 3x - 12 \neq 0
\]

Thus, the final result is:

\[
\frac{4x}{3x-12} = 7 \quad \text{and} \quad 3x \neq 12
\]

So, we conclude with:

\[
\frac{4x}{3x-12} = 7 \quad \text{and} \quad x \neq 4
\]

Answer 2

Can you pls make it shorter

Answer 3

Certainly! The equation \(\frac{4x}{3x-12} + 3 = 10\) can be rewritten as:

\[
\frac{4x}{3x-12} = 7 \quad \text{and} \quad 3x - 12 \neq 0
\]

This is equivalent to:

\[
\frac{4x}{3x-12} = 7 \quad \text{and} \quad x \neq 4
\]