# Thread: Sove simple equation doubt

1. ## Sove simple equation doubt

I'm solving this:
Code:
3 – 7 * (1 - 2x) = 5 – (x + 9)
And am trying this way:
Code:
3- 7 * (1 - 2x) = 5 - (x + 9)
3 - 7 ..?? ??   = 5 - x - 9)
What should be done in the part I put those question marks?

I'm really lost.

Thanks in advance for any help.

2. ## Re: Sove simple equation doubt

Do you know the distributive law?
In general: $\displaystyle a\cdot (b+c)=a\cdot b+a\cdot c$

Use it to expand $\displaystyle -7\cdot (1-2x)=...$

3. ## Re: Sove simple equation doubt

So, I should do:

$\displaystyle 3 - 7 . (1 - 2x) = 5 - (x + 9)$
$\displaystyle 3 - 7 . 1 - 7 . 2x = 5 - x - 9)$
$\displaystyle 3 - (-7) - 14x = 5 - x - 9$
$\displaystyle -10x = ...$

I'm lost...

4. ## Re: Sove simple equation doubt

You have to pay attention with the signs:
$\displaystyle 3-7\cdot (1-2x)=5-(x+9)$
$\displaystyle \Leftrightarrow 3-7\cdot 1 -7\cdot (-2x)=5-x-9$
$\displaystyle \Leftrightarrow 3-7+14x=5-x-9$
$\displaystyle \Leftrightarrow 3-7-5+9=-x-14x$
$\displaystyle \Leftrightarrow 0=-15x$
$\displaystyle \Leftrightarrow x=0$

5. ## Re: Sove simple equation doubt

I was doing:
Code:
3 - 7 * (1 - 2x) = 5 - (x + 9)
3 - 7 * 1 - 7 * (-2x) = ...
3 - (-7) - 14x = ...
When I should be doing:
Code:
3 - 7 * (1 - 2x) = 5 - (x + 9)
3 - 7 * 1 - 7 * (-2x) = ...
3 - 7 - 14x = ...
Why don't I put -7 inside parentheses?

6. ## Re: Sove simple equation doubt

If you expand:
$\displaystyle 7(1-2x)=7-14x$
And the LHS is:
$\displaystyle 3-[7(1-2x)]=3-(7-14x)=3-7+14x$

If you expand:
$\displaystyle -7(1-2x)=-7+14x$
Now, the LHS is:
$\displaystyle 3+[-7(1-2x)]=3-7+14x$