Write a compound inequality that represents the following phrase. Graph the solutions.
all real numbers that are between -2 and 7
-2 ≤ x ≤ 7
The compound inequality that represents the given phrase is -2 < x < 7.
To graph the solutions on a number line, draw a line with an open circle at -2 and an open circle at 7. Shade the region between the two open circles to represent the set of real numbers that are between -2 and 7. The shaded region indicates the solution set.
To represent the phrase "all real numbers that are between -2 and 7" as a compound inequality, we first need to identify the inequality symbols that correspond to the given conditions.
We know that the numbers must be between -2 and 7, which means they must be greater than -2 and less than 7.
The inequality symbol for "greater than" is ">" and the inequality symbol for "less than" is "<".
Combining these, the compound inequality would be:
-2 < x < 7
To graph the solutions, we can create a number line and mark the values -2 and 7. Then, shade the area between -2 and 7 since all real numbers within this range satisfy the condition. The endpoints (-2 and 7) should not be included in the solution set.