Question

Identify the inequality that represents the following problem. One less than twice a number is no less than five. What is the solution set?

1 - 2n ≥ 5
2n - 1 ≥ 5
2n - 1 > 5
1 - 2n > 5

Answer 1

the last one is ur answer

Answer 2

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

Explanation:

We are dealing here with two problems:

1. First, to determine which mathematical statement represents "One less than twice a number is no less than five".
2. 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
`\\1 - 2n`, 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:

`\\1 - 2n > 5`.

Second Part: Finding the solution set

The solution set for this inequality is as follows:

`\\ 1-2n > 5` ⇒

Subtract -1 from each member of the inequality:

`\\ 1-1-2n>5-1` ⇒
`\\ -2n>5-1` ⇒
`\\ -2n>4`

Multiply each member of the inequality by
`\\-(1)/(2)` (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:

`\\ -(1)/(2)*(-2)*n< -(1)/(2)*4`

`\\ 1*n< -(1)/(2)*4`

`\\ n < -2`

The solution set is then
`\\ n< -2`, 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
`\\1 - 2n > 5` is
`\\ (-\infty, -2)`.