Solve $7 f+12 \geq 5 f+4$
Answer (1)
Subtract 5 f from both sides: 2 f + 12 ≥ 4 .
Subtract 12 from both sides: 2 f ≥ − 8 .
Divide both sides by 2: f ≥ − 4 .
The solution to the inequality is f ≥ − 4 .
Explanation
Understanding the Inequality We are given the inequality 7 f + 12 g e q 5 f + 4 . Our goal is to isolate f on one side of the inequality to find the solution set.
Subtracting 5 f from Both Sides First, we subtract 5 f from both sides of the inequality: 7 f + 12 − 5 f g e q 5 f + 4 − 5 f
This simplifies to: 2 f + 12 g e q 4
Subtracting 12 from Both Sides Next, we subtract 12 from both sides of the inequality: 2 f + 12 − 12 g e q 4 − 12
This simplifies to: 2 f g e q − 8
Dividing by 2 Finally, we divide both sides of the inequality by 2: 2 2 f g e q 2 − 8
This simplifies to: f g e q − 4
So the solution to the inequality is f g e q − 4 .
Examples
Imagine you're saving money, and you want to know how many weeks it will take to have more than a certain amount. If you save $7 each week and start with $12, and you want to have more than what you'd have if you saved $5 each week and started with only $4, this inequality helps you figure out how many weeks you need to save. Understanding and solving linear inequalities is useful in many real-life situations, such as budgeting, comparing costs, and planning.
