https://file.aiquickdraw.com/mathbot/file/17272197461132fz2lquy.jpg

The equation shown in the image is:

\[
\frac{3}{4}x - a = 2b
\]

We are tasked with solving this equation for \( x \).

### Step-by-step solution:

1. **Start by isolating the \( x \)-term:**
   \[
   \frac{3}{4}x = a + 2b
   \]

   Add \( a \) to both sides to move \( a \) to the right-hand side.

2. **Multiply both sides by the reciprocal of \( \frac{3}{4} \), which is \( \frac{4}{3} \):**
   \[
   x = \frac{4}{3}(a + 2b)
   \]

This is the expression for \( x \). Now let's compare it with the given answer choices.

### Simplified Options:
- Option 1: \( x = \frac{3(a + 12b)}{2} \)
- Option 2: \( x = \frac{4(a + 2b)}{3} \)
- Option 3: \( x = \frac{30a + 20b}{5} \)
- Option 4: \( x = \frac{10(a + b)}{2} \)

Clearly, **Option 2** matches the form of the solution we derived:

\[
x = \frac{4(a + 2b)}{3}
\]

### Answer:
**Option 2** is the correct answer.

---

Would you like more details, or have any questions?  
Here are five related questions:

1. How would the solution change if the coefficient of \( x \) were different?
2. Can you derive the formula if \( a \) were on the right side instead?
3. What if the equation was \( \frac{5}{6}x - a = 2b \), how would you solve for \( x \)?
4. How can we check if our solution is correct for a specific value of \( a \) and \( b \)?
5. How do you solve a literal equation when there are variables on both sides?

**Tip**: Always check your work by plugging your solution back into the original equation!

Solve the equation \( \frac{3}{4}x - a = 2b \) for \( x \).

Learn how to solve the literal equation \( \frac{3}{4}x - a = 2b \) by isolating the variable x. This solution involves key algebraic techniques like multiplication by reciprocals and isolating terms. Perfect for students in Grades 9-11.

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