which inequality symbol produces an inequality with a finite number of nonsolutions
Well, if we're talking about inequalities, the symbol that produces an inequality with a finite number of nonsolutions would have to be the "equals" sign. Because when you use the equals sign in an inequality, you're basically saying that there is only one solution that satisfies the given condition. And since there is a finite number of solutions, there can only be a finite number of nonsolutions too. It's a bit like saying, "Hey, there's only one answer to this problem, don't even bother trying to come up with something else!" So, in other words, the humble "equals" sign wants to keep things nice and finite.
The inequality symbol that produces an inequality with a finite number of non-solutions is the strict inequality symbol. This includes '<' (less than) and '>' (greater than). These symbols indicate that the two sides of the inequality are not equal and that there is a strict boundary between the solutions and non-solutions.
The inequality symbol that produces an inequality with a finite number of nonsolutions is the strict inequality symbol "<" or ">".
When solving an inequality, we often aim to find the range of values that make the inequality true. In some cases, the inequality can have an infinite number of solutions, meaning there are infinitely many values that satisfy the inequality. However, when we use strict inequality symbols "<" or ">", it indicates that the values are not included in the solution set, resulting in a finite number of nonsolutions.
For example, consider the inequality 2x < 8. Here's how we can find the solution:
1. Start by isolating x. Divide both sides of the inequality by 2: (2x)/2 < 8/2, simplifying to x < 4.
2. Since the strict inequality symbol "<" is used, we need to exclude 4 from the solution. Therefore, the solution is all real numbers less than 4, but not including 4.
In this case, the inequality has a finite number of nonsolutions because we exclude the value 4 from the solution set. This pattern holds true for any strict inequality where we exclude specific values from the range of solutions.
The inequality symbol that produces an inequality with a finite number of nonsolutions is the strict inequality symbol "<" or ">".
For example, the inequality x > 3 has a finite number of nonsolutions because there are only a limited number of values of x that are not greater than 3. Any value of x that is greater than 3 satisfies the inequality, while any value of x that is less than or equal to 3 does not.
On the other hand, the non-strict inequality symbol "<=" or ">=" produces an inequality with an infinite number of nonsolutions. For example, the inequality x >= 3 includes all values of x that are greater than or equal to 3, which is an infinite set of values.