Solving Inequality Problem to Find Satisfying Numbers

What is the inequality representation of the given relationship involving a number so that three times two less than that number is greater than or equal to five times the number? What are the numbers that satisfy this inequality?

Final answer:

The given condition can be translated to the inequality 3(n - 2) ≥ 5n. Solving it results in n ≤ -3. Hence, all numbers less than or equal to -3 satisfy the given condition.

Explanation:

The question is asking for the number n that satisfies the inequality three times two less than a number is greater than or equal to five times the number. In mathematical terms, this translates to 3(n - 2) ≥ 5n.

To solve for n, you start by expanding the left side of the inequality, resulting in 3n - 6 ≥ 5n. By rearranging the equation, you get -6 ≥ 2n. Dividing by 2 leads to n ≤ -3.

Therefore, the numbers that satisfy the inequality are all numbers less than or equal to -3.

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