In the equation \(ax+b=0\), when \(a, x, \text{ and } b\) are integers and \(x\) and \(b\) are positive, \(a\) must be:
Try testing some values, such as \(x=2 \text{ and } b=3\).
$$ a(2)+3 = 0 $$
$$ a = -\frac{3}{2} $$
\(a\) is negative and a factor of \(b\). Note the factors of \(b=3\) in this case can be \(-\dfrac{3}{2}\) and \(-2\).
\(-\dfrac{3}{2}\) would not be considered a multiple of \(b=3\) since multiples can only be integer multiples.
$$ ax+b=0 $$
$$ ax = -b $$
$$ -ax = b $$
\(a\) and \(x\) are factors of \(b\) since their product is \(b\). Since \(x\) and \(b\) are positive, \(a\) must be negative.