\( \begin{array}{ll}\text { 2. } & 3 y-5=10 \\ \text { 3. } & 4 a+1=-11 \\ \text { 4. } & 6 b-3=9 \\ \text { 5. } & 5 c+8=3\end{array} \)

To tackle these equations, let’s solve each one step by step! For the first equation \(3y - 5 = 10\), add 5 to both sides to get \(3y = 15\), then divide by 3 and find \(y = 5\). Next, in \(4a + 1 = -11\), subtract 1 from both sides to yield \(4a = -12\). Dividing by 4 gives us \(a = -3\). Moving to \(6b - 3 = 9\), add 3 to both sides to arrive at \(6b = 12\). Dividing by 6 results in \(b = 2\). Finally, for \(5c + 8 = 3\), subtract 8 from both sides to get \(5c = -5\), and dividing by 5 gives \(c = -1\). So, in summary: - \(y = 5\) - \(a = -3\) - \(b = 2\) - \(c = -1\) Mathematics has a rich history that dates back thousands of years! Ancient civilizations, like the Egyptians and Babylonians, laid the groundwork for algebraic equations. They used simple calculations and developed methods that are surprisingly similar to what we use today. Their innovations paved the way for modern mathematics, making it not just practical but an art form! In the real world, understanding algebra is really useful. It helps in various professions like engineering, economics, and even everyday planning like budgeting your finances. Each time you set a budget or plan a trip, there’s some algebra involved! Knowing how to solve these equations equips you with problem-solving skills that are applicable in countless everyday scenarios. So, whether you’re at work or at home, the art of solving equations can come in handy!