of \( -2 m-15 \geq-2.4 ? \)

To solve the inequality \( -2m - 15 \geq -2.4 \), first, isolate \( m \). Start by adding 15 to both sides: \(-2m \geq 12.6\). Next, divide by -2, remembering to flip the inequality sign: \(m \leq -6.3\). So, \( m \) must be less than or equal to -6.3 for the inequality to hold true! Now, onto a real-world application: this kind of inequality can represent a scenario where you're trying to determine a price point below which expenses exceed income. For example, if you’re managing a budget where \( -2m \) represents your expenses and you need to stay under a certain amount (like -2.4), you’d use similar inequalities to strategize your spending effectively. On the problem-solving side, a common mistake is forgetting to flip the inequality sign when multiplying or dividing by a negative number. Always keep this in mind, as it can completely change the outcome of the inequality!