Solve. \( 5 x-10 \leq 20 \) \( (-\infty, 2] \) \( (-\infty, 2) \) \( (-\infty, 6] \) \( (-\infty, 6) \)

To solve the inequality \( 5x - 10 \leq 20 \), first add 10 to both sides to get \( 5x \leq 30 \). Then, divide both sides by 5, resulting in \( x \leq 6 \). This means the solution set is all values of \( x \) that are less than or equal to 6, which is represented as \( (-\infty, 6] \). Understanding inequalities is essential in various fields, such as economics, where they can help model constraints in budget conditions. For instance, if a certain budget allows for only spending up to $6 on a single item, you can easily use inequalities to determine the maximum quantity you can purchase without exceeding your budget, keeping it fun by imagining what you could buy with your allowance! A common mistake when solving inequalities is forgetting to reverse the inequality sign when multiplying or dividing by a negative number. If you ever find yourself working with \( -5x \), make sure to flip that inequality sign when you solve! This little trick helps you avoid frustrating errors and leads you to the right solutions—no more throwing your pencil in despair!