Thread: Distributing and simplifying

4(3x-5)= -2(-x+8)

I got 10x= 4
= 2.5

Originally Posted by vaironxxrd

4(3x-5)= -2(-x+8)

I got 10x= 4
= 2.5

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

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

Originally Posted by Prove It

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

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

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

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:
$\displaystyle \frac{\frac{10x}{4}}{10}$?
Because that's not just $\displaystyle x$ but $\displaystyle \frac{\frac{10x}{4}}{10}=\frac{x}{4}$

Originally Posted by Siron

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

So your telling me its basically 10x/4/10? That looks weird

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: $\displaystyle \dfrac{10}{4} x = 1$. From here you'd need to divide both sides by 10/4: $\displaystyle x = \dfrac{1}{\left(\frac{10}{4}\right)}$ and since we divide fractions by "flip n multiply" the RHS is the same as $\displaystyle 1 \times \dfrac{4}{10} = \dfrac{4}{10}$



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

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