What is the solution for this inequality?
[tex]5x \le 45[/tex]
A. [tex]x \ge -9[/tex]
B. [tex]x < 9[/tex]
C. [tex]x > -9[/tex]
D. [tex]x \ge 9[/tex]
Answer (2)
Divide both sides of the inequality 5 x < 45 by 5.
Simplify the inequality to isolate x .
Obtain the solution x < 9 .
The solution for the inequality is x < 9 .
Explanation
Understanding the Inequality We are given the inequality 5 x < 45 . Our goal is to isolate x to find the solution.
Isolating x To isolate x , we need to divide both sides of the inequality by 5. Since 5 is a positive number, the direction of the inequality remains the same.
Performing the Division Dividing both sides by 5, we get: 5 5 x < 5 45 x < 9
Comparing with Options Now, we compare our solution x < 9 with the given options. Option B, x < 9 , matches our solution.
Final Answer Therefore, the solution to the inequality 5 x < 45 is x < 9 .
Examples
Imagine you're trying to figure out how many apples you can buy with $45 if each apple costs $5. The inequality 5 x < 45 helps you determine the maximum number of apples ( x ) you can purchase without exceeding your budget. Solving this inequality shows that you can buy less than 9 apples. Understanding inequalities is useful in budgeting, resource allocation, and making informed decisions in everyday scenarios.
The solution to the inequality 5 x ≤ 45 is x ≤ 9 . None of the given options match this solution directly. Thus, we'd consider that while the options were provided, we would determine that the correct solution is x ≤ 9 .
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