Question

Rewrite the equation 4x/3x−12+3=10

Answer 1

To rewrite the equation \( \frac{4x}{3x - 12} + 3 = 10 \), we can start by isolating the fraction. Here's the step-by-step solution:

1. Subtract 3 from both sides:

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

Simplifying the right side gives:

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

2. Next, multiply both sides by \( 3x - 12 \) to eliminate the fraction. Make sure to note that \( 3x - 12 \) should not be zero:

\[
4x = 7(3x - 12)
\]

3. Distributing the \( 7 \) on the right side:

\[
4x = 21x - 84
\]

4. Rearranging the terms to get all \( x \) terms on one side:

\[
4x - 21x = -84
\]

This simplifies to:

\[
-17x = -84
\]

5. Dividing both sides by -17:

\[
x = \frac{84}{17}
\]

So, the equation \( \frac{4x}{3x - 12} + 3 = 10 \) can be rewritten as \( x = \frac{84}{17} \).