1. **State the problem:** We have a balanced scale with two sides. On the left side, there are 3 identical rectangular bricks, and the total weight is 14 kg. On the right side, there are 5 identical rectangular bricks, and the total weight is 4 kg. We need to find the weight of one rectangular brick. 2. **Set up the equation:** Let the weight of one brick be $x$ kg. The total weight on the left side is $3x$ and on the right side is $5x$. Since the scale is balanced, the total weights on both sides are equal: $$3x = 5x$$ 3. **Analyze the problem:** The problem states the scale is balanced, but the given total weights 14 kg and 4 kg do not match the number of bricks times the weight $x$ if $x$ is the same for both sides. 4. **Re-examine the problem statement:** The problem says "if all bricks on both sides have equal weight," and the total weights on the sides are equal. This means the total weight on the left side equals the total weight on the right side: $$14 = 4$$ This is a contradiction, so the problem likely means the total weight on the left side is 14 kg, and on the right side is 4 kg, but the bricks are identical. 5. **Correct interpretation:** The left side has 3 bricks weighing 14 kg total, so each brick weighs: $$x = \frac{14}{3}$$ The right side has 5 bricks weighing 4 kg total, so each brick weighs: $$x = \frac{4}{5}$$ Since the bricks are identical, these must be equal: $$\frac{14}{3} = \frac{4}{5}$$ This is false, so the problem must mean the total weight on both sides is equal, and the bricks are identical. 6. **Set the equation for balance:** Let $x$ be the weight of one brick. Left side weight: $3x$ Right side weight: $5x$ Since the scale is balanced: $$3x = 5x$$ 7. **Solve the equation:** Subtract $3x$ from both sides: $$3x - 3x = 5x - 3x$$ $$0 = 2x$$ Divide both sides by 2: $$\cancel{\frac{0}{2}} = \cancel{\frac{2x}{2}}$$ $$0 = x$$ 8. **Interpretation:** The weight of one brick is 0 kg, which is impossible. 9. **Conclusion:** The problem as stated is inconsistent or missing information. **Final answer:** The problem cannot be solved with the given data because the weights and number of bricks do not correspond to a balanced scale with identical bricks.