Write $14p + 18$ in terms of $7p$ and $9$. How does $14p + 18$ relate to $7p + 9$?

If $14p + 18$ can be written as a multiple of $7p + 9$, how can you use the fact that $7p + 9 = 30$ to find the new value?

In Desmos, type the expression 14*((30-9)/7)+18 and look at the value it outputs. This uses $p = (30-9)/7$ from the equation $7p + 9 = 30$ and then evaluates $14p + 18$ for that $p$.

You are told that $7p + 9 = 30$. This means whatever $p$ is, when you plug it into $7p + 9$, the result is 30.

Compare $14p + 18$ to $7p + 9$.

Notice that:

• $14p = 2 \cdot 7p$
• $18 = 2 \cdot 9$

So you can rewrite:

From the problem, $7p + 9 = 30$. Substitute this into the expression you just found:

Now evaluate $2(30)$:

So the value of $14p + 18$ is $60$.