The solution to the problem \( -4(x-3) \leq 16 \) is that \( x \) is greater than or equal to

To solve the inequality \( -4(x-3) \leq 16 \), first, we'll distribute the -4, giving us \( -4x + 12 \leq 16 \). Next, we isolate the variable by subtracting 12 from both sides: \( -4x \leq 4 \). Finally, divide both sides by -4, remembering to flip the inequality sign, which results in \( x \geq -1 \). So, the solution is that \( x \) is greater than or equal to -1. The inequalities are foundational in understanding mathematical relationships. For example, they determine ranges of values in real-life scenarios such as budgeting, where you need to understand how much more money you can spend without going over your budget. Inequalities help to create safe limits! If you'd like to dive deeper into inequalities, consider resources like online math courses or videos that tackle similar problems. Websites like Khan Academy or PatrickJMT can offer comprehensive explanations and practice problems that offer an engaging way to master these concepts.