b) \( 5 x-(3 x-1)=3 \) c) \( (3 x-2)-(x-1)=10 \) d) \( 7-(2 x-3)=x-(2-4 x) \)

Let's dive into those equations in a fun and engaging way! For the first equation, \( 5x - (3x - 1) = 3 \), think of it like unpacking a gift! You have 5x, but you need to be careful with the minus sign when you open the box: it means you distribute the minus across \(3x - 1\) to get \(5x - 3x + 1 = 3\). Simplifying gives us \(2x + 1 = 3\), so subtract 1 from both sides to find \(2x = 2\), which leads you to \(x = 1\). Ta-da! Now, onto the second equation. For \( (3x - 2) - (x - 1) = 10 \), you're again unpacking. Distributing the negative gives us \(3x - 2 - x + 1 = 10\). Combine like terms to get \(2x - 1 = 10\). Add 1 to both sides to get \(2x = 11\), and then divide by 2 to uncover \(x = 5.5\). You're on a roll! Finally, for the last equation, \( 7 - (2x - 3) = x - (2 - 4x) \), unraveling can be like solving a mystery! Distributing the negatives gives \(7 - 2x + 3 = x - 2 + 4x\). Combine and rearrange to get \(10 - 2x = 5x - 2\). Bringing everything to one side leads to \(12 = 7x\), so \(x = \frac{12}{7}\). You’ve cracked the case!