Question

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.
Which of the following is the solution set of the problem?
A) (-00, -3)
B) (-2,- 3]
C) [-3, -20)
D) (-3, 00)

Answer 1

To solve the given problem, we need to translate the given statement into an inequality. The solution set is n ≥ -3.

Step-by-step explanation:

To solve the given problem, we need to translate the given statement into an inequality. Let's break it down step by step.

First, we define the number as 'n'.

The phrase 'two less than a number' can be represented as 'n - 2'.

So, 'Three times two less than a number' is '3(n - 2)'.

The phrase 'five times the number' is '5n'.

Next, we translate the given condition: 'Three times two less than a number is greater than or equal to five times the number' can be written as '3(n - 2) ≥ 5n'.

Now, we can solve this inequality to find the solution set.

Start by distributing the 3 on the left side: '3n - 6 ≥ 5n'.

Subtract '3n' from both sides: '-6 ≥ 2n'.

Divide both sides by 2 (keeping in mind the rule that dividing by a negative number flips the inequality sign): '-3 ≤ n'.

So, the solution set is: 'n ≥ -3'.

Therefore, the correct option is D) (-3, 0).