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 >= 5n
6 - n >= 5n
add n to both sides.
3(n – 2) >5n is the correct answer
The inequality that represents the given relationship is: 3(n-2) ≥ 5n.
Now, let's solve the inequality step by step to find the values of n that satisfy the given conditions.
Step 1: Distribute the 3 on the left side of the inequality:
3n - 6 ≥ 5n
Step 2: Subtract 3n from both sides of the inequality to isolate the variable on one side:
-6 ≥ 5n - 3n
Simplifying the right side:
-6 ≥ 2n
Step 3: Divide both sides of the inequality by 2 to solve for n:
-6/2 ≥ 2n/2
Simplifying:
-3 ≥ n
Therefore, all values of n that satisfy the given conditions are n ≤ -3 or in interval notation (-∞, -3].
To represent the given relationship, you can write the inequality as:
3n - 2 ≥ 5n
Now, let's solve the inequality to find the values of n that satisfy the given conditions.
First, let's simplify the equation:
3n - 2 ≥ 5n
Combine like terms by subtracting 3n from both sides:
-2 ≥ 2n
Divide both sides by 2:
-1 ≥ n
So, the inequality representing the given relationship is n ≤ -1.
Therefore, all the numbers that satisfy the conditions are any number less than or equal to -1.