Factors and Multiples Question 7

In the equation $ax+b=0$ , when $a, x, \text{ and } b$ are integers and $x$ and $b$ are positive, $a$ must be:

negative and a factor of

b

negative and a multiple of

b

positive and a factor of

b

positive and a multiple of

b

positive and equal to

b

Approach 1

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.

Approach 2

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.