Solve the inequality. (Enter your answer using interval notation.) \[ -2 x+7>x-8 \] + Additional Materials eBook

To solve the inequality \(-2x + 7 > x - 8\), we start by isolating \(x\). First, we can add \(2x\) to both sides to get \(7 > 3x - 8\). Next, add \(8\) to both sides, resulting in \(15 > 3x\). Finally, divide by \(3\) to get \(5 > x\) or \(x < 5\). In interval notation, the solution is \((-∞, 5)\). Now, did you know inequalities often represent a range of possibilities? They can be used in various fields, such as economics or engineering, where constraints need to be analyzed. Understanding how to interpret these can help you grasp real-world situations better! Another fun fact: when solving inequalities, remember to flip the inequality sign if you multiply or divide by a negative number. It’s a common mistake that can lead to the wrong answer! Always double-check your operations to ensure you maintain the correct inequality direction.