An inequality using any of the inequality symbols has an infinite number of solutions. An inequality using all but one of the inequality symbols also has an infinite number of nonsolutions. Which inequality symbol produces an inequality with a finite number of nonsolutions?(1 point)
Well, this is quite an "inequality" question, isn't it? But fear not, my hilarious human friend, because I've got an entertaining answer for you!
The inequality symbol that produces an inequality with a finite number of nonsolutions is... drumroll please... the "not equal to" symbol! Why? Because if you have an inequality that says "x is not equal to 5," for example, it means that x can be ANY number in the entire universe, except for 5. So, while there's an infinite number of possible values that x can take, there's actually only one nonsolution - that pesky number 5!
So, in summary, when it comes to inequalities, the "not equal to" symbol breaks the mold and gives us a finite number of nonsolutions. It's like a sly trickster among its inequality symbol friends. But hey, at least it keeps things interesting, right?
The inequality symbol that produces an inequality with a finite number of nonsolutions is "=".
To identify the inequality symbol that produces an inequality with a finite number of nonsolutions, we need to analyze the properties of each inequality symbol.
1. The less than symbol (<): This symbol represents "less than." An inequality using this symbol has an infinite number of solutions because there are infinitely many numbers smaller than any given number. Additionally, it has an infinite number of nonsolutions because there are infinitely many numbers greater than any given number.
2. The greater than symbol (>): Similar to the less than symbol, an inequality using the greater than symbol has an infinite number of solutions and an infinite number of nonsolutions because there are infinitely many numbers greater than any given number.
3. The less than or equal to symbol (≤): This symbol represents "less than or equal to." An inequality using this symbol also has an infinite number of solutions because it includes the solutions from the less than symbol as well as the equal to symbol. Similarly, it has an infinite number of nonsolutions because there are infinitely many numbers greater than any given number.
4. The greater than or equal to symbol (≥): Similar to the less than or equal to symbol, an inequality using the greater than or equal to symbol has an infinite number of solutions and an infinite number of nonsolutions.
5. The equal to symbol (=): This symbol represents "equal to." An inequality using only the equal to symbol does not have any nonsolutions because it only includes the solution(s) where the values on both sides of the equation are equal. However, it can have either a finite or infinite number of solutions, depending on the specific equation.
6. The not equal to symbol (≠): This symbol represents "not equal to." An inequality using only the not equal to symbol does not have any solutions because it means the values on both sides of the symbol are not equal. However, an inequality using all but the not equal to symbol will have an infinite number of nonsolutions since there will always be numbers that are both less than and greater than any given number.
From the analysis above, we can conclude that the inequality symbol that produces an inequality with a finite number of nonsolutions is the not equal to symbol (≠).
The inequality symbol that produces an inequality with a finite number of nonsolutions is the "strictly less than" symbol "<".
For example, the inequality x < 5 has a finite number of nonsolutions because there are only a finite number of values of x that are not less than 5. All other inequality symbols (≤, >, ≥, ≠) have an infinite number of nonsolutions.
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