1. We are given the proportion $150 : 33 = x : 126$ and need to find the value of $x$. 2. The formula for solving proportions is to cross-multiply: $$a : b = c : d \implies a \times d = b \times c$$ 3. Applying this to our problem: $$150 \times 126 = 33 \times x$$ 4. Calculate the left side: $$150 \times 126 = 18900$$ 5. So, $$18900 = 33 \times x$$ 6. To isolate $x$, divide both sides by 33: $$x = \frac{18900}{33}$$ 7. Show the cancellation step: $$x = \frac{\cancel{18900}}{\cancel{33}}$$ (we simplify the fraction by dividing numerator and denominator by 3) 8. Simplify numerator and denominator: $$x = \frac{6300}{11}$$ 9. Perform the division: $$x = 572.7272...$$ (approximately) 10. Final answer: $$x \approx 572.73$$