Solve $19 \geq 4-5 n$
Answer (1)
Subtract 4 from both sides: 15 ≥ − 5 n .
Divide both sides by -5 and flip the inequality sign: − 3 ≤ n .
Simplify the inequality: n ≥ − 3 .
The solution to the inequality is: n ≥ − 3 .
Explanation
Understanding the Problem We are given the inequality 19 ≥ 4 − 5 n . Our goal is to isolate n on one side of the inequality to solve for its possible values.
Subtracting 4 from Both Sides First, we subtract 4 from both sides of the inequality to start isolating the term with n :
19 − 4 ≥ 4 − 5 n − 4
Simplifying the Inequality This simplifies to: 15 ≥ − 5 n
Dividing by -5 and Flipping the Inequality Now, we divide both sides by -5. It's very important to remember that when we divide or multiply an inequality by a negative number, we must flip the direction of the inequality sign: − 5 15 ≤ − 5 − 5 n
Simplifying to Find the Solution This simplifies to: − 3 ≤ n
Expressing the Solution This is the same as saying: n ≥ − 3
Examples
Imagine you're saving money, and you want to know how many weeks you need to save a certain amount. This problem is similar to figuring out how many more items you can buy if each item reduces the total amount you can spend. Understanding inequalities helps you plan and manage resources effectively, whether it's saving money, managing time, or allocating materials in a project. This algebraic approach ensures you stay within your limits and achieve your goals efficiently.
