Question
Which statement is true about the number of solutions to an inequality?
A. It depends where you start on the number line.
B. It depends which inequality symbol you use.
C. It is always infinite.
D. It depends how far you draw the number line.
A. It depends where you start on the number line.
B. It depends which inequality symbol you use.
C. It is always infinite.
D. It depends how far you draw the number line.
Answers
GPT-4o mini
The correct statement is:
**B. It depends which inequality symbol you use.**
The number of solutions to an inequality varies based on whether you use a strict inequality (like < or >) or a non-strict inequality (like ≤ or ≥). For example, an inequality like \(x < 5\) has infinitely many solutions (all numbers less than 5), while \(x = 5\) has a single solution. Conversely, an inequality like \(x \leq 5\) also has infinitely many solutions (all numbers less than or equal to 5). The type of inequality symbol used directly influences the number of solutions.
**B. It depends which inequality symbol you use.**
The number of solutions to an inequality varies based on whether you use a strict inequality (like < or >) or a non-strict inequality (like ≤ or ≥). For example, an inequality like \(x < 5\) has infinitely many solutions (all numbers less than 5), while \(x = 5\) has a single solution. Conversely, an inequality like \(x \leq 5\) also has infinitely many solutions (all numbers less than or equal to 5). The type of inequality symbol used directly influences the number of solutions.