Match the inequality in each exercise in Column I with its equ...

Question

Match the inequality in each exercise in Column I with its equivalent interval notation in Column II. x≤6

Matching exercise with inequalities and interval notations alongside number lines illustrating solution sets.

Accepted Answer

Hey everyone here we are asked to write the equivalent interval notation for the given inequality, X is less than or equal to positive four. So, to begin solving this problem, we first need to represent this given inequality on a number line. So we can plot a few values on our number line, I'll place zero in the middle and then to the right. Well our positive values we'll just have five and 10. And then for the negative values we'll just have negative five and negative 10. And now we need to look at our inequality and we see we have the value four when we need to make sure this value is on our number line. So we can plot it just before the positive five and now we can go ahead and assess our given inequality. Well, we see that X is less than or equal to four. So we have a non strict inequality and therefore this positive four gets a bracket on its value. And now we go, we see that X can also be less than four. So we go from positive four to negative infinity. And we need to note that infinity signs are always excluded. So it gets closed by a parenthesis. And now with this information identified, we can go ahead and write out our equivalent interval notation. So we see that X is within new negative infinity, which again gets closed by a parentheses to positive four, which is closed by a bracket. And this is our final answer here, which is answer choice B. Thanks for watching. I hope you found this video helpful, and I'll see you again next time.

Match the inequality in each exercise in Column I with its equivalent interval notation in Column II. x≤6

Key Concepts

Inequalities

Interval Notation

Set Representation of Solutions

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