Solving the equation $-5a = 15$: is it possible to multiply a negative number by a positive and make it positive?

Question

I'm stuck with a question which says this $$-5a = 15$$ What is $a$? I'm confused; is it possible to multiply a negative number by a positive and make it positive?

Answer 1

What would you do to solve for $a$ if the equation were $$5a=15,$$ instead? What if it were $$2a=15,$$ instead? What if it were $$\pi a=15,$$ instead? Picking up on the pattern? You'll do the same thing, here.

(By the way, the answer to the question in your title is "no," but I'm not sure what it has to do with the body of the question.)

Answer 2

You're intuition is correct so far. The product of a negative number with a positive number is always negative. The trick is you can't tell if the number represented by a variable is positive or negative just by looking at the letter.

You have the equation $-5a = 15$. Here the $-5$ and the $a$ are multiplied and the result of that multiplication is $+15$. This tells us that $a$ must be a negative number.

Now that we know that $a$ is negative we just need to figure out which negative number will produce 15 when multiplied by $-5$. You probably remember that $3\cdot 5 = 15$. This means that $(-3)(-5)=15$. So the answer for $a$ is $\boxed{a=-3}$.

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A more efficient way to solve this is to use division right away.

Whenever you have, $-5 a = 15$ , you can solve for $a$ by dividing the $15$ by $-5$. $a=-15/5 \Rightarrow a=-3$.

To do this you have to remember you sign rules. In this example we used the fact that the result of dividing a positive number by a negative number is a negative number.

Answer 3

$$-5a=(-5)a=15\implies a=\frac{15}{(-5)}=-3.$$