Three times two less than a number is greater than or equal to five times the number. Find all of the numbers that satisfy the given conditions. Let \( n= \) a number. Choose the inequality that represents the given relationship. \( 3(2)-n \geq 5 n \) \( 3(2-n) \geq 5 n \) \( 3 n-2 \geq 5 n \) \( 3(n-2) \geq 5 n \) DoNEIV

To solve the problem, we need to translate the given statement into an inequality. The statement is: "Three times two less than a number is greater than or equal to five times the number." 1. **Identify the variable**: Let \( n \) be the number. 2. **Translate the phrase "two less than a number"**: This can be expressed as \( n - 2 \). 3. **Translate "three times two less than a number"**: This becomes \( 3(n - 2) \). 4. **Translate "five times the number"**: This is simply \( 5n \). 5. **Set up the inequality**: The statement says that "three times two less than a number is greater than or equal to five times the number." This can be written as: \[ 3(n - 2) \geq 5n \] Now, we can solve the inequality \( 3(n - 2) \geq 5n \). ### Step-by-step solution: 1. **Distribute the 3**: \[ 3n - 6 \geq 5n \] 2. **Rearrange the inequality**: Subtract \( 3n \) from both sides: \[ -6 \geq 5n - 3n \] This simplifies to: \[ -6 \geq 2n \] 3. **Divide both sides by 2** (note that dividing by a positive number does not change the inequality): \[ -3 \geq n \] or equivalently, \[ n \leq -3 \] ### Conclusion: The solution to the inequality is that all numbers \( n \) that satisfy the condition are those less than or equal to -3. Thus, the final answer is: \[ n \leq -3 \]