Question
The inequality \( -\frac{9}{4} \leq x \) in interval notation is \( \square \)
Ask by Norton Young. in the United States
Feb 27,2025
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Answer
The inequality \( -\frac{9}{4} \leq x \) in interval notation is \( \left[-\frac{9}{4}, \infty \right) \).
Solution
Solve the equation \( -\frac{9}{4} \leq x \).
Solve the inequality by following steps:
- step0: Solve for \(x\):
\(-\frac{9}{4}\leq x\)
- step1: Swap the sides:
\(x\geq -\frac{9}{4}\)
The inequality \( -\frac{9}{4} \leq x \) in interval notation is \( \left[-\frac{9}{4}, \infty \right) \).
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Simplify this solution Bonus Knowledge
The inequality \( -\frac{9}{4} \leq x \) means that \( x \) can take any value greater than or equal to \( -\frac{9}{4} \). In interval notation, we express this as \( \left[-\frac{9}{4}, \infty\right) \). Here, the square bracket indicates that \( -\frac{9}{4} \) is included in the set of solutions. When working with inequalities, it's easy to make mistakes like forgetting to include the endpoint or misreading the direction of the inequality sign. A common tip is to always double-check the signs and ensure you’re using brackets or parentheses correctly. Remember, brackets denote inclusion while parentheses exclude the endpoint!
