Find the solution set of 𝑥 over
four minus three equals negative five in the set of all integers.
First, we remember that this symbol
is the set of all integers. And then, we can turn our attention
to solving for 𝑥. If 𝑥 over four minus three equals
negative five, we want to try to isolate 𝑥, to get 𝑥 by itself. And the first thing we should do in
order to do that is add three to both sides. Once we do that, we’ll get 𝑥 over
four is equal to negative two because negative five plus three equals negative
We know that 𝑥 over four means 𝑥
divided by four. Some value divided by four equals
negative two. To find out what that value is, we
need to do the opposite. If 𝑥 is being divided by four, we
need to multiply both sides of the equation by four, like this. Four times 𝑥 over four equals 𝑥,
and negative two times four equals negative eight. At this point, we should check and
see if that’s true.
Is negative eight divided by four
minus three equal to negative five? Negative eight divided by four is
negative two. And negative two minus three is
negative five. This means that 𝑥 is equal to
negative eight. But here our solution needs to be
given as a set notation. That’s the curly brackets. And the solution set for this
equation is just negative eight.