1. ## How do you work out this equation please?

I've recently started teaching myself algebra for a work related course and whilst working through some practice papers online I came across the equation:

-2 = -(n-8)

I have had no problems working out multi step equations so far but this one has stumped me. I know the answer is 10 but I need to know HOW to work it out.

Any help will be gently appreciated! Thanks.

2. ## Re: How do you work out this equation please?

Hello Sb2011.
First of all, multiply both sides by -1: $\displaystyle (-2)(-1)=-(n-8)(-1)$ and you will get $\displaystyle 2=n-8$,
now isolate n by adding 8 to both sides, $\displaystyle 2+8=n-8+8$, you will get $\displaystyle n=10$.
I hope this helps.

3. ## Re: How do you work out this equation please?

Thanks for your answer DIOGYK, yes that helps but could someone please explain in simple terms how you knew and why you multiply each side by -1? Is there a basic rule for this type of equation? Thanks again!

4. ## Re: How do you work out this equation please?

Originally Posted by Sb2011
Thanks for your answer DIOGYK, yes that helps but could someone please explain in simple terms how you knew and why you multiply each side by -1? Is there a basic rule for this type of equation? Thanks again!
You're welcome.

I multiplied both sides by -1 because both sides were negative and negative times negative would make both sides positive. This is the rule: Equation stays valid (doesn't change) if you apply some operation (like addition, multiplication ...) to both sides of the equation. You could still do this problem without multiplying by -1 but it's easier to see the next step when you have positive numbers (for me).

You could do this problem without multiplying by "-1" this way:
$\displaystyle -2=-(n-8)$, This is the same as $\displaystyle -2=-1(n-8)$, now distribute -1 in -> $\displaystyle -2=-1*n+(-1)(-8)$ or $\displaystyle -2=-n+8$, add n to both sides -> $\displaystyle -2+n=-n+8+n$ or $\displaystyle -2+n=8$, now add 2 to both sides to isolate n -> $\displaystyle -2+n+2=8+2$ or $\displaystyle n=10$. I hope I didn't confuse you.

5. ## Re: How do you work out this equation please?

Always try to work your way backwards towards the variable you are trying to solve for. Think of it like, you are trying to rescue a man buried under a pile of rubble. Remove the rubble one by one. In this case, n is your man and the rubble is the bunch of operations that surround the n.

On the very outside of the rubble is a negative sign. How do you remove it? Perform the opposite step, multiply both sides of the equation by negative 1. This will lead to:

2 = (n-8)

Then there is still some 'rubble' left in the form of subtracting 8. So to undo that, you need to add 8 to both sides:

2 + 8 = n

n = 10

The key in this analogy is that you need to remove, or undo, what's on the very outside first, before the rest, similar to when you are trying to rescue someone. The multiplication by -1 was on the very outside, so you need to deal with that first.