$$ \frac{4+4 \times 18 - 6 - 8}{123 \times 6 - 146 \times 5} = x $$

### Concept & Logic This problem requires careful execution of arithmetic operations according to the BODMAS rule, followed by decimal conversion. You must accurately multiply large numbers in the denominator and simplify the entire fraction before finding the exact decimal value. ### Step-by-Step Solution * **Step 1:** Simplify the numerator. Expression: $4 + 4 \times 18 - 6 - 8$ First, perform the multiplication: $4 \times 18 = 72$. The expression becomes: $4 + 72 - 6 - 8$. Now, process addition and subtraction from left to right: $76 - 6 - 8 = 70 - 8 = 62$. Numerator $= 62$. * **Step 2:** Simplify the denominator. Expression: $123 \times 6 - 146 \times 5$ Perform the multiplications: $123 \times 6 = 738$ $146 \times 5 = 730$ Subtract the results: $738 - 730 = 8$. Denominator $= 8$. * **Step 3:** Form the fraction and solve for the decimal. $$ x = \frac{62}{8} $$ Reduce the fraction by dividing by 2: $$ x = \frac{31}{4} $$ Convert to decimal: $\frac{31}{4} = 7 \frac{3}{4} = 7.75$. ### Exam Strategy & Shortcut For $146 \times 5$, use the shortcut of multiplying by 10 and dividing by 2: $1460 \div 2 = 730$. This is much faster than standard vertical multiplication. When you arrive at $\frac{62}{8}$, look at the options. You know $8 \times 7 = 56$ and $8 \times 8 = 64$. Therefore, the answer must be between 7 and 8. The only option that fits this estimation is 7.75, eliminating the need to do the final long division manually. ### Common Pitfall A standard arithmetic error occurs in the denominator calculation $123 \times 6$. If rushed, students might calculate it as 728 instead of 738, leading to a denominator of $-2$ and throwing off the entire result. Double-check single-digit multiplications carefully. ### Final Answer **Therefore, the correct answer is 7.75.**