Solve $\frac{294 \div 14 \times 5 + 11}{x} = 8^2 \div 5 + 1.7$

### Concept & Logic This problem requires strict adherence to the **BODMAS** rule (Brackets, Orders, Division, Multiplication, Addition, Subtraction). The equation must be simplified by evaluating the numerator on the left and the entire expression on the right before isolating $x$. ### Step-by-Step Solution * **Given Equation:** $$\frac{294 \div 14 \times 5 + 11}{x} = 8^2 \div 5 + 1.7$$ * **Step 1: Simplify the Left-Hand Side (LHS) Numerator** According to BODMAS, perform division first, then multiplication, then addition. $$294 \div 14 = 21$$ $$21 \times 5 = 105$$ $$105 + 11 = 116$$ So, the LHS becomes $\frac{116}{x}$. * **Step 2: Simplify the Right-Hand Side (RHS)** Resolve the exponent (order) first, then division, then addition. $$8^2 = 64$$ $$64 \div 5 = 12.8$$ $$12.8 + 1.7 = 14.5$$ So, the RHS becomes $14.5$. * **Step 3: Solve for $x$** Equate the simplified sides: $$\frac{116}{x} = 14.5$$ $$x = \frac{116}{14.5}$$ To remove the decimal, multiply the numerator and denominator by $10$: $$x = \frac{1160}{145}$$ Dividing gives: $$x = 8$$ ### Exam Strategy & Shortcut Simplify expressions in chunks mentally. For LHS: $294/14 = 21$; $21 \times 5 = 105$; $105+11 = 116$. For RHS: $64/5 = 12.8$; $12.8+1.7 = 14.5$. Now you have $116 = 14.5 \times x$. Instead of long division, check the unit digits or use multiples. $14.5 \times 2 = 29$. $29 \times 4 = 116$. Therefore, $x = 2 \times 4 = 8$. ### Common Pitfall Failing to follow BODMAS in the numerator is the most common mistake (e.g., multiplying before dividing or adding before multiplying). Also, arithmetic errors frequently happen when dividing by decimals like $14.5$. ### Final Answer **Therefore, the correct answer is 8.**