Solve the Inequality |2x-1| > -10: Key Insights

Let's solve the problem:
Step 1: Recognize that the inequality we are dealing with is $\left|2x-1\right| > -10$.
Step 2: Consider the nature of absolute values: for any real $x$, $\left|2x-1\right|$ is always non-negative (i.e., $\geq 0$).
Step 3: Observe that the right side of the inequality, $-10$, is negative. Therefore, the inequality $\left|2x-1\right| > -10$ is always true because $\left|2x-1\right|$ as a non-negative quantity will always be greater than any negative number.
Step 4: Since the inequality condition always holds true, this means that the statement is valid for all $x$.

Therefore, the correct answer is that the inequality holds for all $x$.

The solution to the problem is For all x.