How to read $\exists x \forall y \exists z((x + y)z = 1)$?

Question

$$\exists x \forall y \exists z((x + y)z = 1)$$

How can I translate this expression to English? And is the statement true or false? (for numbers in $\Bbb R$).

$z=1$ is the part that confuses me.

Answer 1

It translates as:

There exists an $x$ such that whatever $y$ you choose you can find an $z$ such that $x+y$ multiplied by $z$ equals $1$.

It is false because no matter what value $x$ has, whenever $y=-x$, $x+y$ multiplied by $z$ is zero.