To qualify for a summer internship program, an applicant’s age, , in years, must be at least but no more than . Which inequality represents all possible ages that satisfy this requirement?
For inequality wording questions, first translate each phrase into a simple inequality: “at least” means , “at most” or “no more than” means , and decide whether the endpoint is included. Then combine the conditions, if needed, into a single compound inequality that both must be true at once. Finally, match that combined inequality to the answer choice, paying close attention to whether the symbols are or and or so you don’t accidentally exclude allowed endpoint values.
Hints
Focus on “at least 16”
Ask yourself: if someone is "at least 16" years old, can they be exactly 16, or do they have to be older than 16? What inequality symbol matches that idea?
Focus on “no more than 20”
If someone is "no more than 20" years old, can they be exactly 20, or must they be younger than 20? Which inequality symbol shows that?
Combine both requirements
The age must satisfy both phrases at once. Which answer choice shows ages that are between 16 and 20 while also allowing the endpoints that are permitted by the wording?
Desmos Guide
Graph the inequality conditions
In Desmos, use for the age. Type x >= 16 on one line and x <= 20 on another line. You will see the number line shaded between 16 and 20, including solid dots or closed shading at 16 and 20.
Match the shading to an answer choice
Look at the part of the number line that is shaded in Desmos: it includes all from 16 through 20, with the endpoints included. Compare this to each answer choice and pick the one whose inequality describes exactly that set of -values.
Step-by-step Explanation
Translate “at least 16”
"At least 16" means the age must be 16 or greater.
In inequality form, this is:
- , which is the same as .
So one condition is that is not smaller than 16, and 16 itself is allowed.
Translate “no more than 20”
"No more than 20" means the age must be 20 or less.
In inequality form, this is:
- .
So the second condition is that cannot be larger than 20, and 20 itself is allowed.
Combine both conditions into one inequality
The age must satisfy both conditions at the same time:
- (at least 16)
- (no more than 20)
We can write this as a single compound inequality:
This inequality represents all possible ages from 16 up to 20, including both 16 and 20, so is the correct choice.