Need simple(?) algebra help please!

I'm not sure how to solve for these types of algebra equations. Could you please tell me the steps required?

1. 170(x) - 70 (1-x) = 0. Solve for x. X should be 0.292 but I am having trouble finding out how.

The next equation:

2. -6(0.5) - 20(x) + 14(1-0.5-x) = 0

Thanks so much!

Re: Need simple(?) algebra help please!

Hello clc98,

When solving these types of equations it's best to gather up all the x's in one place. So,

Step 1. Multiply out any brackets:

$\displaystyle -70(1-x)$ becomes $\displaystyle ((-70)(1) - (-70)(x))$ which then becomes $\displaystyle (-70 + 70x)$

the last equation is because $\displaystyle -(-70)=+70$, i.e., a minus multiplied by a minus gives a plus.

So after step 1 we have $\displaystyle 170x - 70 + 70x = 0$.

Step 2. Put all the x's together. 170x + 70x becomes 240x because I can add the x's (I can add the terms that are alike).

So now the equation becomes,

$\displaystyle 240x - 70 = 0$

Step 3. Get all the x terms on one side and all the normal numbers on the other. We can add 70 to both sides of the equation to get rid of the -70.

So the equation becomes,

$\displaystyle 240x - 70 + 70 = 0 + 70$

which becomes

$\displaystyle 240x= 70$

Step 4. Now we want to get the x on its own. We divide both sides by 240,

$\displaystyle \frac{240x}{240}=\frac{70}{240}$

$\displaystyle \frac{240x}{240}$ becomes just $\displaystyle x$ and $\displaystyle \frac{70}{240}$ becomes 0.29166666...

So we have,

$\displaystyle x=0.29166666....$.