Let's follow your instructions to isolate the variable term after combining like terms, focusing on the terms \(3x\) and \(-\frac{2}{9}x\).
Starting from the original equation:
\[
\frac{3x - 1}{5} - \frac{2}{9}x = \frac{124}{5}
\]
Step 1: Combine Like Terms
As you mentioned, the terms that can be combined are \(3x\) and \(-\frac{2}{9}x\).
- Convert \(3x\) to a form that allows us to combine with \(-\frac{2}{9}x\):
\[
3x = \frac{3 \cdot 9}{9}x = \frac{27}{9}x
\]
Now, substitute this back into the equation:
\[
\frac{27x}{9} - \frac{2}{9}x = \frac{3x - 1}{5}
\]
- Combine the \(x\) terms:
\[
\frac{27x - 2x}{9} = \frac{3x - 1}{5}
\]
\[
\frac{25x}{9} = \frac{3x - 1}{5}
\]
Step 2: Isolate the Variable Term
Now, let’s isolate the variable term \(3x\) by removing the fractions. We can do this by cross-multiplying:
\[
25x \cdot 5 = (3x - 1) \cdot 9
\]
This leads to:
\[
125x = 27x - 9
\]
Step 3: Solve for \(x\)
Now, let's collect the \(x\) terms on one side. We'll subtract \(27x\) from both sides:
\[
125x - 27x = -9
\]
\[
98x = -9
\]
Dividing both sides by 98 gives us:
\[
x = -\frac{9}{98}
\]
Choices Evaluation
You asked which among the choices of \(-\frac{2}{9}\), \(\frac{1}{5}\), or \(3\) is related:
However, focusing on your previous question regarding combining terms:
- The combined terms \(3x\) and \(-\frac{2}{9}x\) yield \( \frac{25x}{9} \).
- If you would like to relate that back to your choices, they do not directly equate to the isolated \(x\).
Among the provided options, none of these values directly ties to the solution we derived: \(-\frac{9}{98}\).
Conclusion
If you are strictly asking for which one of the specified answers \(-\frac{2}{9}\), \(\frac{1}{5}\), or \(3\) is the result of isolating terms here, none directly relate to the variable isolation. If needing a choice solely based on context:
- The correct answer for your specified context is: -2/9, as it relates closest to the negative outcome from combining \(-\frac{2}{9}x\) originally.
If this needs clarification or adjustment, feel free to specify!