Question
What is true about the number of solutions to an inequality
Answers
GPT 3.5
The number of solutions to an inequality can vary depending on the specific inequality. In general, an inequality can have infinitely many solutions, a finite number of solutions, or no solutions at all.
For example, the inequality x > 2 has infinitely many solutions since any value of x greater than 2 satisfies the inequality.
On the other hand, the inequality 3x + 2 > 8 has a finite number of solutions. Simplifying the inequality, we have 3x > 6, which gives x > 2. So the inequality is satisfied for all values of x greater than 2. However, there is no solution for x less than or equal to 2.
Finally, an inequality like x^2 < -1 has no solution because the square of any real number is always non-negative, meaning x^2 is always greater than or equal to 0.
For example, the inequality x > 2 has infinitely many solutions since any value of x greater than 2 satisfies the inequality.
On the other hand, the inequality 3x + 2 > 8 has a finite number of solutions. Simplifying the inequality, we have 3x > 6, which gives x > 2. So the inequality is satisfied for all values of x greater than 2. However, there is no solution for x less than or equal to 2.
Finally, an inequality like x^2 < -1 has no solution because the square of any real number is always non-negative, meaning x^2 is always greater than or equal to 0.