If 1) \( 3 x-5(2-x)=54 \) 2) \( 0,5(2 y-1)-(0,5-0,2 y)+1=0 \) 3) \( \frac{9}{2}-\frac{a}{8}=5 \) 4) \( \frac{5 x}{9}+\frac{x}{3}, 4=0 \)

Let's dive into the equations, solve them step-by-step, and sprinkle in some fun wisdom along the way! 1) For the equation \( 3 x - 5(2 - x) = 54 \), simplify it to get \( 3x + 5x - 10 = 54 \), leading to \( 8x - 10 = 54 \). Add 10 to both sides, giving you \( 8x = 64 \). Thus, \( x = 8 \). It's like finding your missing puzzle piece! 2) In the second equation, \( 0.5(2y - 1) - (0.5 - 0.2y) + 1 = 0 \), distribute and combine like terms to find \( 1y - 0.5 + 0.2y = -1 \). Solve to get \( 1.2y - 0.5 = -1 \) leading you to \( 1.2y = -0.5 \). Finally, \( y = -\frac{5}{12} \). A little negative vibe never hurt anyone! 3) Moving on to \( \frac{9}{2} - \frac{a}{8} = 5 \), convert \( 5 \) into eighths: \( \frac{40}{8} \). Rearranging to get \( \frac{9}{2} - \frac{40}{8} = \frac{36 - 40}{8} = -\frac{4}{8} \), gives you \( a = 8 \). Who knew fractions could keep things spicy? 4) Finally, for \( \frac{5x}{9} + \frac{x}{3} = 4 \), convert \( \frac{x}{3} \) into ninths: \( \frac{3x}{9} \). Combine and you have \( \frac{8x}{9} = 4 \). Multiplying both sides by 9 gives \( 8x = 36 \), leading to \( x = 4.5 \). Math doesn’t have to be boring; it’s all about finding balance, just like that perfect slice of cake! 🎂