Rewrite the following as an inequality statement.
$(1,\infty )$

• A. $x\(\ge\)1$
• B. $x\(\le\)1$
• C. $x>1$
• D. $x<1$

Answer: (C)

Verified step by step guidance

1. Identify the interval notation given: \(\left(1, \infty\right)\). This represents all real numbers greater than 1 but not including 1 itself.
2. Recall that a parenthesis '(' in interval notation means the endpoint is not included, so the inequality will be strict (using > or <, not ≥ or ≤).
3. Since the interval starts at 1 and goes to infinity, the inequality will involve \(x\) being greater than 1.
4. Write the inequality statement corresponding to the interval: \(x > 1\).
5. Verify that this inequality matches the interval by noting that \(x\) can be any number larger than 1, but not equal to 1.