Identify the inequality that represents the following problem. One less than twice a number is no less than five. What is the solution set? 2 n - 1 > 5
2 n - 1 ≥ 5
1 - 2 n ≥ 5
1 - 2 n > 5

is the last one

1 - 2n > 5. The solution set is (-∞, -2)

Step-by-step explanation:

e are dealing here with two problems:

First, to determine which mathematical statement represents "One less than twice a number is no less than five".

Second, solve n, that is, the solution set for the numbers that solve the inequality.

First Part: Identifying the inequality

"One less than twice a number" can be written as  , where n is the unknown number.

If it is not less than five, thus it is greater (no less) than five. Then, the symbol here is  " > " (greater).

As a result: "One less than twice a number is no less than five" could be rewritten as "One less than twice a number is greater than five", or:

.

Second Part: Finding the solution set

The solution set for this inequality is as follows:

⇒

Subtract -1 from each member of the inequality:

⇒  ⇒  

Multiply each member of the inequality by  (or divide each member by -2). We have to remember here that when we multiply or divide an inequality by a negative number (-n), this inverts the inequality, that is:

The solution set is then , which is any value less than -2 (not including -2, because is < and not ≤), and we have infinite negative numbers with such a characteristic. We can write it mathematically as an interval notation:

Solution set for  is .

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