Match the inequality in each exercise in Column I with its equiva-lent interval notation in Column II. -2

Question

Match the inequality in each exercise in Column I with its equiva-lent interval notation in Column II. -2<x≤6

Accepted Answer

Hey everyone here we are asked to write the equivalent interval notation for the given inequality where we have negative five is less than X, which is less than or equal to nine. So to begin solving this problem, we first want to represent the give Inequality on a number line. So we can start by writing out our number line here and now I'll include a few values. The middle value will be zero into the right hand side. Our positive values, I'll just have five and 10. And then for the negative values I'll just have negative five and negative 10. And now looking at our inequality, we have the negative five plotted on our number line. But we also need to include the other value here, which is nine. So I'll place it just before the 10 and now we can go ahead and start assessing our given inequality. So we see that negative five is less than X. So this inequality is strict and therefore negative five gets a parentheses on its value here and now moving on we go from negative five to positive nine. And we see in our inequality that X is less than or equal to nine. So we have a non strict inequality for nine and therefore nine gets closed off with a bracket. So now with this information identified, we can go ahead and write our equivalent interval notation. So here we see that X is within negative five, which again is closed by a parentheses to positive nine, which is closed off by a bracket. So this is our final answer here, which is answer choice C. Thanks for watching. I hope you found this video helpful, and I'll see you again next time.

Verified Solution

Key Concepts

Inequalities

Interval Notation

Graphing Inequalities