# Distributing and simplifying

• Sep 9th 2011, 08:09 AM
vaironxxrd
Distributing and simplifying
4(3x-5)= -2(-x+8)

I got 10x= 4
= 2.5
• Sep 9th 2011, 08:13 AM
Prove It
Re: Distributing and simplifying
Quote:

Originally Posted by vaironxxrd
4(3x-5)= -2(-x+8)

I got 10x= 4
= 2.5

\displaystyle \begin{align*} 4(3x-5) &= -2(-x+8) \\ 12x-20 &= 2x-16\\ 10x-20 &= -16\\ 10x &= 4 \\ x &= \frac{4}{10} \\ x &= \frac{2}{5}\end{align*}

I disagree with your answer of $\displaystyle x = 2.5$
• Sep 9th 2011, 08:31 AM
vaironxxrd
Re: Distributing and simplifying
Quote:

Originally Posted by Prove It
\displaystyle \begin{align*} 4(3x-5) &= -2(-x+8) \\ 12x-20 &= 2x-16\\ 10x-20 &= -16\\ 10x &= 4 \\ x &= \frac{4}{10} \\ x &= \frac{2}{5}\end{align*}

I disagree with your answer of $\displaystyle x = 2.5$

Oh so I was pretty close . One more question when 10x/4 you divide by 10 to get x by itself?
• Sep 9th 2011, 09:17 AM
Siron
Re: Distributing and simplifying
Quote:

Originally Posted by vaironxxrd
Oh so I was pretty close . One more question when 10x/4 you divide by 10 to get x by itself?

Do you mean:
$\frac{\frac{10x}{4}}{10}$?
Because that's not just $x$ but $\frac{\frac{10x}{4}}{10}=\frac{x}{4}$
• Sep 9th 2011, 09:41 AM
vaironxxrd
Re: Distributing and simplifying
Quote:

Originally Posted by Siron
Do you mean:
$\frac{\frac{10x}{4}}{10}$?
Because that's not just $x$ but $\frac{\frac{10x}{4}}{10}=\frac{x}{4}$

So your telling me its basically 10x/4/10? That looks weird
• Sep 9th 2011, 10:44 AM
e^(i*pi)
Re: Distributing and simplifying
Quote:

Originally Posted by vaironxxrd
Oh so I was pretty close . One more question when 10x/4 you divide by 10 to get x by itself?

10x/4 has to equal something though. In this case it is equal to 1 because you've brought the 4 from the RHS onto the LHS by division: $\dfrac{10}{4} x = 1$. From here you'd need to divide both sides by 10/4: $x = \dfrac{1}{\left(\frac{10}{4}\right)}$ and since we divide fractions by "flip n multiply" the RHS is the same as $1 \times \dfrac{4}{10} = \dfrac{4}{10}$

From the line $10x = 4$ you can divide both sides by 10 because we want to get x on it's own (which is the same as 1x): $\dfrac{10x}{10} = \dfrac{4}{10}$ and since 10/10 is indeed 1 this is the same as $\dfrac{4}{10}$ which is correct but it's more proper to simplify fractions and so 2/2 was cancelled.

$\dfrac{4}{10} = \dfrac{2 \times 2}{2 \times 5} = \dfrac{2}{5}$.