# What is the solution to 2/3x- 2=-5x +1?

Nov 14, 2016

$x = \frac{9}{17}$

#### Explanation:

Step 1) To solve this problem isolate all terms containing $x$ on one side of the equation and all other terms on the other side of the equation:

$\frac{2}{3} x - 2 + 5 x + 2 = - 5 x + 1 + 5 x + 2$

$\frac{2}{3} x + 5 x = 1 + 2$

$\frac{2}{3} x + 5 x = 3$

Step 2) Get the $x$ terms over a common denominator and then solve for $x$ while keeping the equation balanced:

$\frac{2}{3} x + \left(\frac{3}{3}\right) 5 x = 3$

$\frac{2}{3} x + \frac{15}{3} x = 3$

$\frac{17}{3} x = 3$

$\left(\frac{3}{17}\right) \frac{17}{3} x = 3 \cdot \left(\frac{3}{17}\right)$

$1 x = \frac{9}{17}$

$x = \frac{9}{17}$