Solve: 1/4a + 1/2a + x/3 + 4b/3 + 2x/3 - Combining Mixed Variable Fractions

To solve this problem, we'll follow these steps:

• Step 1: Simplify and combine fractions with $a$.
• Step 2: Simplify and combine terms with $x$.
• Step 3: Express the final simplified algebraic expression.

Now, let's work through each step:
Step 1: Look at the terms with $a$: $\frac{1}{4a} + \frac{1}{2a}$.
Find a common denominator, which is $4$ in this case:

$\frac{1}{4a} + \frac{2}{4a} = \frac{1 + 2}{4a} = \frac{3}{4a}$.

Step 2: Simplify and combine terms with $x$:

$\frac{x}{3} + \frac{2}{3}x = \frac{1x}{3} + \frac{2x}{3} = \frac{3x}{3} = x$.

Step 3: Combine all terms together in the expression. Keep the $b$-related term as it is and combine:

$\frac{3}{4a} + x + \frac{4}{3}b$.

Therefore, the solution to the problem is $\frac{3}{4a} + x + \frac{4}{3}b$, which matches choice 2.