Write a compound inequality that represents each situation. Graph your solution.all real numbers that are greater than –6 but less than 6

A) –6 ≤ x < 6
B) –6 ≤ x ≤ 6
C) –6 < x < 6
D) –6 < x ≤ 6

The compound inequality that represents each situation is –6 < x < 6.

Let's consider the given situation step by step. We know that the numbers should be greater than -6, so we can use the symbol "x > -6" to represent this condition. Additionally, we need the numbers to be less than 6, which can be represented as "x < 6."

Now, we need to combine these two inequalities to represent the whole situation. Since we want both conditions to be true, we should use the "and" condition, which is represented by the symbol "∧" or simply by writing the inequalities side by side.

So, the compound inequality representing the given situation is:

-6 < x < 6

In this compound inequality, x represents any real number that is greater than -6 and less than 6. This means that the numbers between -6 and 6, excluding -6 and 6 themselves, are the solution set for this compound inequality.

Graphically, this can be represented on a number line. We draw a line and mark -6 with an open circle and draw an open circle at 6 as well. Then, we shade the region between -6 and 6 to show that all real numbers within this range satisfy the compound inequality.

So, the correct option is (c).

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