Now look at the words describing how $p$ compares to $15$. Does “no more than $15$” allow $p$ to be equal to $15$, or must it be strictly less than $15$? Which symbol fits: $<$ or $\le$?

Once you know how $p$ relates to $8$ and how it relates to $15$, write both inequalities and think about how to show them together in a single statement. Then choose the option that matches that combined inequality.

From the words, choose a few prices that should be allowed (for example, $9$ and $15$) and a few that should not be allowed (for example, $8$ and $16$).

For each answer choice, replace $p$ with a valid price like $9$ and type that inequality into Desmos (for example, something like $9>8$ or $8<9\le15$, depending on the option). Desmos will tell you whether the statement is true or false. The correct inequality must be true for all valid prices you test.

Now repeat the process with prices that should not be allowed, like $8$ and $16$. For the correct option, Desmos should show the inequality is false for these invalid prices. The answer is the option that is true for all allowed values and false for the disallowed ones.

The problem says the price $p$ is greater than $8$.

• “Greater than $8$” means $p$ must be more than $8$, not equal to $8$.
• In symbols, this is written as $p>8$, which is the same as $8<p$.

So one condition is that $p$ is strictly greater than $8$ (do not include $8$).

The problem also says the price is no more than $15$.

• “No more than $15$” means $p$ can be $15$ or any smaller value, but not larger.
• In symbols, this is written as $p\le15$.

So the second condition is that $p$ is less than or equal to $15$ (this does include $15$).

Both conditions must be true at the same time:

• $p>8$ (greater than $8$), and
• $p\le15$ (no more than $15$).

We can combine these into a single inequality:

This inequality exactly matches answer choice B) $8 < p \le 15$.