Solve for x 7+5x-2=3x-4(3-x) What is x?

Feb 28, 2018

$x = 8.5$

Explanation:

$7 + 5 x - 2 = 3 x - 4 \left(3 - x\right)$
$7 + 5 x - 2 = 3 x - 12 + 4 x$
$2 x = 17$
$x = \frac{17}{2}$
$x = 8.5$

Feb 28, 2018

$x = 8.5$

Explanation:

$5 x + 5 = 3 x - 12 + 4 x$
$5 x + 5 = 7 x - 12$
$17 = 2 x$
$x = 8.5$

Feb 28, 2018

17/2

Explanation:

Let's take the initial equation:
$7 + 5 x - 2 = 3 x - 4 \left(3 - x\right)$
We can simplify the left hand side by adding $7$ and $- 2$
$5 x + 5 = 3 x - 4 \left(3 - x\right)$:
We can simplify the right hand side by multiplying $3$ and $- x$ by $- 4$:
$5 x + 5 = 3 x - 12 + 4 x$
We can simplify again by adding $3 x$ and $- 4 x$:
$5 + 5 x = 7 x - 12$
Now let's subtract $5$ from both sides and subtract $7 x$ from both sides to move all $x$ values to one side of the equation:
$\left(5 + 5 x\right) - 5 = \left(7 x - 12\right) - 5$
$5 x = 7 x - 17$
$\left(5 x\right) - 7 x = \left(7 x - 17\right) - 7 x$
$- 2 x = - 17$
Divide both sides by $- 2$ and we have our answer.
$x = \frac{- 17}{-} 2$
$x = \frac{17}{2}$