What is the solution to the inequality \( \frac{d}{7}+4 \leq 0 \) ? \( (-\infty,-28) \) \( (-\infty,-28] \) \( (28, \infty) \) \( [28, \infty) \)

To solve the inequality \( \frac{d}{7} + 4 \leq 0 \), we first isolate \( d \). Start by subtracting 4 from both sides: \[ \frac{d}{7} \leq -4 \] Next, multiply both sides by 7 (noting that we do not flip the inequality sign since 7 is positive): \[ d \leq -28 \] Thus, the solution to the inequality is \( (-\infty, -28] \). Now, let’s make this journey a bit more interesting: Did you know that linear inequalities, like this one, are closely related to real-world issues like budgeting? For instance, if you’re trying to keep your spending under a certain limit (in this case, related to \( d \)), understanding inequalities can help you track what you can afford without going overboard. In solving inequalities, one common mistake is forgetting to reverse the inequality sign when multiplying or dividing by a negative number. Luckily, in our case, we dealt with a positive number, so we danced through without a hitch! Always double-check the signs during a problem-solving session to maintain your equilibrium!