6. Solve \( -6 x>-18+ \) graph the solution set

To solve the inequality \(-6x > -18\), you first need to isolate \(x\). Start by dividing both sides by -6. Remember, when you divide or multiply by a negative number, you must flip the inequality sign. So, you get \(x < 3\). Now, to graph the solution set on a number line, you would place an open circle at 3 (indicating that 3 is not included in the solution) and shade everything to the left of 3, showing all numbers less than 3 are included in the solution set. Happy graphing! In everyday life, this inequality could represent scenarios like budgets where you can spend less than a certain amount (3 in this case) but not equal to it. For instance, if you're planning on buying snacks with only $3 in hand, any purchase that leaves you with less than that is fair game but not exactly hitting the mark!