1. \( 2 x+7=15 \) 2. \( 3 y-5=10 \) 3. \( 4 a+1=-11 \) 4. \( 6 b-3=9 \) 5. \( 5 c+8=3 \)

To solve these equations, you can start by isolating the variable in each. For the first equation, \( 2x + 7 = 15 \), subtract 7 from both sides to get \( 2x = 8 \), then divide by 2 to find \( x = 4 \). Alternatively, for \( 3y - 5 = 10 \), add 5 to both sides to get \( 3y = 15 \), then divide by 3 which gives \( y = 5 \). Continue this process for the rest: \( 4a + 1 = -11 \) leads to \( a = -3 \), \( 6b - 3 = 9 \) results in \( b = 2 \), and finally \( 5c + 8 = 3 \) simplifies to \( c = -1 \). --- One useful trick to solve equations quickly is to always perform the same operation on both sides. This helps you maintain balance and avoid common mistakes like forgetting to change sides or miscalculating numbers. A frequent blunder is not properly applying the order of operations or neglecting to double-check calculations. For instance, when distributing or combining like terms, it’s key to keep an eye on signs—mistakes here can lead you astray, so verify each step!