if p+pq is 4 times p-pq, which of the following has exactly one value? (pq≠0)
a) p
b) q
c) pq
d) p+pq
e) p-pq

Question

if p+pq is 4 times p-pq, which of the following has exactly one value? (pq≠0) 
a) p
b) q
c) pq
d) p+pq
e) p-pq

anonymous · Answer

$$p+pq=4(p-pq)\
p+pq=4p-4pq\
5pq=3p$$
Since $pq\not=0$, you know that $p\not=0$ and $q\not=0$ (zero product property). So, you can divide both sides by $p$:
$$5q=3$$

anonymous · Answer

@SithsAndGiggles wait so what the answer because i dont know how you continue form 5q=3 unless its q for q=3/5

anonymous · Answer

So you get $q=\dfrac{3}{5}$. Plug that into the original equation and solve for $p$:
$$p+\frac{3}{5}p=4\left(p-\frac{3}{5}p\right)\
\frac{8}{5}p=\frac{8}{5}p$$
You get an identity; this is true for all $p$. It doesn't matter what you plug in for $p$, as long as you have $q=\dfrac{3}{5}$.

This means $p$ does not have exactly one value, and neither does any expression containing $p$.

anonymous · Answer

so p means more than 1 value, so the equation without p is the answer?

anonymous · Answer

Yes, only $q$ has exactly one value. Any "expression" (not equation) containing $p$ would not have one value, since the equation above holds for all $p$ and only one value of $q$.

anonymous · Answer

ok thanx^^