Solve $5 n-9>47-2 n$
Answer (2)
The solution to the inequality 47 - 2n"> 5 n − 9 > 47 − 2 n is 8"> n > 8 . This indicates that any value of n greater than 8 will satisfy the inequality. Hence, you can choose any number greater than 8 as a solution.
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Add 2 n to both sides: 47"> 7 n − 9 > 47 .
Add 9 to both sides: 56"> 7 n > 56 .
Divide both sides by 7: 8"> n > 8 .
The solution to the inequality is 8}"> n > 8 .
Explanation
Understanding the Inequality We are given the inequality 47 - 2n"> 5 n − 9 > 47 − 2 n . Our goal is to isolate n on one side of the inequality to find the solution.
Adding 2n to Both Sides First, let's add 2 n to both sides of the inequality to group the n terms together: 47 - 2n + 2n"> 5 n − 9 + 2 n > 47 − 2 n + 2 n This simplifies to: 47"> 7 n − 9 > 47
Adding 9 to Both Sides Next, we want to isolate the term with n , so we add 9 to both sides of the inequality: 47 + 9"> 7 n − 9 + 9 > 47 + 9 This simplifies to: 56"> 7 n > 56
Dividing by 7 Finally, to solve for n , we divide both sides of the inequality by 7: \frac{56}{7}"> 7 7 n > 7 56 This simplifies to: 8"> n > 8
Final Answer Therefore, the solution to the inequality 47 - 2n"> 5 n − 9 > 47 − 2 n is 8"> n > 8 . This means that any value of n greater than 8 will satisfy the original inequality.
Examples
Imagine you're saving money for a new video game that costs $47. You already have some money, but you need to earn more. Suppose you earn $5 per week, but you spend $9 each week on snacks. Your friend earns $2 per week but doesn't spend any money. The inequality helps you determine how many weeks it will take for your total savings to be greater than your friend's savings plus the cost of the video game. Solving inequalities like this helps in financial planning and making informed decisions about savings and expenses.
