How do you solve 2/3(3x-5)-1/2(4x+3)=1/4(2x-1)-1/12?

Nov 6, 2015

$x = - 9$

Explanation:

The first step in this situation is to distribute all values outside of parenthesis

$\frac{2}{3} \cdot \left(3 x\right) = 2 x$
$\frac{2}{3} \cdot \left(- 5\right) = - \frac{10}{3}$

(The subtraction here is distributed as a negative)

$- \frac{1}{2} \cdot \left(4 x\right) = - 2 x$
$- \frac{1}{2} \cdot \left(3\right) = - \frac{3}{2}$

$\frac{1}{4} \cdot \left(2 x\right) = \frac{1}{2} x$
$\frac{1}{4} \cdot \left(- 1\right) = - \frac{1}{4}$

This leaves us with:

$2 x - \frac{10}{3} - 2 x - \frac{3}{2} = \frac{1}{2} x - \frac{1}{4} - \frac{1}{12}$

Combine all like terms (like terms have the same variables attached) (There is a lot of fractional addition but I'm assuming you can calculate those yourself c: )

$- \frac{29}{6} = \frac{1}{2} x - \frac{1}{3}$

Add $\frac{1}{3}$ to both sides

$- \frac{29}{6} + \frac{1}{3} = \frac{1}{2} x - \frac{1}{3} + \frac{1}{3}$

$- \frac{27}{6} = \frac{1}{2} x$

Multiply both sides by 2

$- \frac{27}{6} \cdot 2 = \frac{1}{2} x \cdot 2$

$- \frac{27}{3} = x$

Simplify

$x = - 9$

You can check your answer by substituting this value for x in the equation (you need to distribute to solve anyway so I won't repeat that step)
$2 \left(- 9\right) - \frac{10}{3} - 2 \left(- 9\right) - \frac{3}{2} = \frac{1}{2} \left(- 9\right) - \frac{1}{4} - \frac{1}{12}$

Simplify
$- 18 - \frac{10}{3} + 18 - \frac{3}{2} = - \frac{9}{2} - \frac{1}{4} - \frac{1}{12}$

$- \frac{29}{6} = - \frac{19}{4} - \frac{1}{12}$

$- \frac{29}{6} = - \frac{58}{12}$

$- \frac{29}{6} = - \frac{29}{6}$