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!