Answer:
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 .
