Solve $19 \geq 4-5 n$
Answer (2)
Subtract 4 from both sides: 19 − 4 g e 4 − 5 n becomes 15 g e − 5 n .
Divide both sides by -5 and flip the inequality sign: − 5 15 l e − 5 − 5 n .
Simplify: − 3 l e n .
Rewrite the inequality: n g e − 3 . The solution is n g e − 3 .
Explanation
Understanding the Inequality We are given the inequality 19 g e 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 g e 4 − 5 n − 4
Simplifying the Inequality This simplifies to: 15 g e − 5 n
Dividing by -5 and Flipping the Inequality Now, we divide both sides by -5. Remember that when we divide or multiply an inequality by a negative number, we must reverse the direction of the inequality sign: − 5 15 l e − 5 − 5 n
Simplifying Further This simplifies to: − 3 l e n
Final Solution We can rewrite this inequality as: n g e − 3 This means that n is greater than or equal to -3.
Examples
Understanding inequalities is crucial in many real-world scenarios. For example, if you're budgeting your expenses, you might use an inequality to determine how much you can spend each week while still saving a certain amount. Similarly, in science, inequalities can help define the range of acceptable values for experimental conditions to ensure a reaction occurs safely and effectively. Inequalities are also used in optimization problems to find the best possible solution within given constraints, such as maximizing profit or minimizing costs.
To solve the inequality 19 ≥ 4 − 5 n , we first isolate n by subtracting 4 and then dividing by -5, which flips the inequality. The solution is n ≥ − 3 , meaning n can be -3 or any number greater than that.
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