How many solutions does the following equation have? \( 5 x+8-7 x=-4 x+1 \) Choose 1 answer: (A) No solutions (B) Exactly one solution (C) Infinitely many solutions Show Calculator

To solve the equation \( 5x + 8 - 7x = -4x + 1 \), we first simplify both sides. Combine like terms on the left side: \(-2x + 8 = -4x + 1\) Now, add \(4x\) to both sides: \(-2x + 4x + 8 = 1\) \(2x + 8 = 1\) Next, subtract \(8\) from both sides: \(2x = 1 - 8\) \(2x = -7\) Now, divide by \(2\): \(x = -\frac{7}{2}\) Since we arrived at a single value for \(x\), the answer is (B) Exactly one solution. To engage further, did you know that one of the fascinating aspects of linear equations is that they can represent real-world scenarios, such as sales and revenue projections? Understanding how to manipulate these equations enables professionals to make informed decisions based on data trends! If you're keen to dabble even deeper, exploring the field of algebra can be incredibly rewarding. Learning more about quadratic equations and their visual representation on graphs reveals even more about how different variables interact. Pick up a fun algebra textbook, and you'll be amazed at what you can unlock with just a little mathematical magic!