if x<5 and x>c, give a value of c such that there are no solutions to the compound inequality.explain why there are no solutions?
The value of c could be 5 or any number greater than 5.
The solution is the intersection of both solution sets of the given inequalities.
The solutions of the compound inequality must be solutions of both inequalities.
A number cannot be both less than 5 and greater than 5 at the same time.
To find a value of c such that there are no solutions to the compound inequality, we need to consider the conditions given: x < 5 and x > c.
Let's break it down step by step:
1. Start with the condition x < 5. This means that x can take any value that is less than 5. For example, x could be 4, 3, 2, or even a negative number.
2. Next, consider the condition x > c. This means that x must be greater than some unknown value c. In other words, x has to be on the right side of c on the number line.
To find a value of c such that there are no solutions, we need to make sure that no matter how small c is, x will always be less than 5. In other words, we need to choose a value of c such that there is no overlap between the values of x that satisfy both conditions.
Since x < 5 for any x that is less than 5, we need to choose a value of c that is less than 5. Let's say c = 4.
Now, if we substitute c = 4 into the compound inequality (x < 5 and x > c), we get:
x < 5 and x > 4
This implies that x has to be both less than 5 and greater than 4, which is not possible. No number can satisfy both conditions simultaneously. Therefore, there are no solutions to the compound inequality when c = 4.
In summary, when c = 4, there are no solutions to the compound inequality (x < 5 and x > c) because there is no overlap between the values of x that satisfy both conditions.
To find a value of c such that there are no solutions to the compound inequality x < 5 and x > c, we need to ensure that there is no overlap between the two inequalities.
Since x < 5, any value of c greater than or equal to 5 will ensure that x > c has no solutions. This is because if c is greater than or equal to 5, then x cannot be greater than c.
For example, let's take c = 6. In this case, the compound inequality becomes x < 5 and x > 6. Since no number can be both less than 5 and greater than 6, there are no values of x that satisfy this compound inequality.
Therefore, by choosing a value of c such as c = 5 or any value greater than 5, we can ensure that there are no solutions to the compound inequality x < 5 and x > c.