Write a compound inequality that represents the following phrase. Graph the solutions.
all real numbers that are between -2 and 7
A. - 2 < n < 7 B. - 2 <= n < 7
C. - 2 < n <= 7 D. - 2 <= n <= 7
The correct compound inequality that represents the given phrase is D. -2 <= n <= 7.
To graph the solutions, we will first graph the number line. Then, we will mark the points -2 and 7 on the number line and shade the interval between them. The shaded region represents all the real numbers that are between -2 and 7.
<--o--------------o-----------------------------------o-->
-2 7
The shaded region between the two points -2 and 7 represents the solutions to the compound inequality -2 <= n <= 7.
The correct answer is option A: -2 < n < 7.
To represent the phrase "all real numbers that are between -2 and 7" as a compound inequality, we use the symbols "<" and ">" to indicate that the number is less than or greater than a specific value. The inequality represents an open interval between two values, which means that the endpoints -2 and 7 are not included in the solution set.
Graphically, a number line would help to visualize the solution set. The numbers between -2 and 7, but not including -2 and 7, would be shaded on the number line.
The compound inequality -2 < n < 7 represents the correct range of numbers.
To represent the phrase "all real numbers that are between -2 and 7" as a compound inequality, we can use the combination of both an inequality involving the greater than (>) symbol and an inequality involving the less than (<) symbol.
Denoting "n" as the variable representing the real numbers, we know that "n" must be greater than -2 and less than 7. Therefore, the correct compound inequality that represents this phrase is:
A. -2 < n < 7
To graph the solutions, we can plot a number line with -2 and 7 as open circles (since the inequalities are strict), and shade the region between them to indicate all the valid solutions.