# How do you solve 4x + 2( 8- 3x ) = 12x?

May 16, 2018

$x = \frac{8}{7}$

#### Explanation:

Ok first you need to get the $x$'s on to one side and the numbers on their own on the over, so first expanding the bracket you get

$4 x + 16 - 6 x = 12 x$

Once we collect like terms we end up with

$- 2 x + 16 = 12 x$

Now what we do to one side, we do to the other, so if we add $2 x$ to get rid of the $- 2 x$, we have to also add $2 x$ to the $12$ so we end up with

$16 = 14 x$

And supposedly you want just $x$, so we have to divide both sides by $14$, which is

$x = \frac{16}{14} = \frac{8}{7} \approx 1.4286$

May 16, 2018

Simplify the expression, rearrange terms, and then solve to find $x = \frac{8}{7}$

#### Explanation:

First, we'll simplify. We could multiply both the terms that are in the parentheses by the coefficient (2), but note that the other terms outside of the parentheses are divisible by 2. For this, I elected to divide both sides by 2, which eliminates the need for the parentheses:

$\frac{4 x + 2 \left(8 - 3 x\right)}{2} = \frac{12 x}{2}$

$2 x + \left(8 - 3 x\right) = 6 x$

$2 x + 8 - 3 x = 6 x$

Next, we'll combine like terms:

$8 + x \left(2 - 3\right) = 6 x$

$8 - x = 6 x$

Next, we rearrange by adding $x$ to both sides:

$8 \cancel{- x} \textcolor{red}{\cancel{+ x}} = 6 x \textcolor{red}{+ x}$

$8 = x \left(6 + \textcolor{red}{1}\right)$

$8 = 7 x$

Finally, we divide through by $x$'s coefficient:

$\frac{8}{\textcolor{red}{7}} = \frac{\cancel{7} x}{\textcolor{red}{\cancel{7}}}$

color(green)(x=8/7~=1.1429