$$4\frac{3}{7} - 1\frac{3}{14} = x + 2\frac{3}{28}$$

### Concept & Strategy This is a linear equation containing mixed fractions. The strategy is to isolate the variable $x$ on one side of the equation, then separate the resulting expression into whole numbers and fractional parts to simplify efficiently. Notice that the denominators (7, 14, 28) are multiples of each other, making the common denominator obvious. ### Step-by-Step Solution * **Step 1:** Isolate the variable $x$. Move $2\frac{3}{28}$ to the left side by subtracting it. $$x = 4\frac{3}{7} - 1\frac{3}{14} - 2\frac{3}{28}$$ * **Step 2:** Split the expression into whole numbers and fractions. Whole numbers: $(4 - 1 - 2)$ Fractions: $(\frac{3}{7} - \frac{3}{14} - \frac{3}{28})$ * **Step 3:** Evaluate the whole numbers. $4 - 1 - 2 = 1$ * **Step 4:** Evaluate the fractions using the LCM of 28. Convert $\frac{3}{7}$ to $\frac{12}{28}$ Convert $\frac{3}{14}$ to $\frac{6}{28}$ The fraction expression becomes: $\frac{12}{28} - \frac{6}{28} - \frac{3}{28}$ $\frac{12 - 6 - 3}{28} = \frac{3}{28}$ * **Step 5:** Combine the results. Final Answer $= 1 + \frac{3}{28} = 1\frac{3}{28}$ ### Exam Strategy & Shortcut Since the denominators scale perfectly ($7 \times 2 = 14$, $14 \times 2 = 28$), you can solve the fractions almost entirely in your head. Just think in terms of 28ths: $12 - 6 - 3 = 3$. The whole numbers are trivial: $4 - 1 - 2 = 1$. The answer assembles itself instantly. ### Common Pitfall When shifting $2\frac{3}{28}$ across the equals sign, students sometimes forget to invert the sign of BOTH the whole number and the fraction. Subtracting a mixed number means subtracting the whole part AND subtracting the fractional part. ### Final Answer **Therefore, the correct answer is 1\frac{3}{28}.**