# How do you solve 3/4x - 6 = 1/2x - 9 ?

Apr 11, 2016

$x = - 12$

#### Explanation:

$\textcolor{b l u e}{\frac{3}{4} x} - 6 = \textcolor{b l u e}{\frac{1}{2} x} - 9$

$\textcolor{b l u e}{\frac{3}{4} x - \frac{1}{2} x} = - 9 + 6$

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

$\frac{3}{4} x - \frac{2}{4} x = - 3$

$\frac{1}{4} x = - 3$

$x = - 3 \cdot 4$

$x = - 12$

Apr 11, 2016

$x = - 12$

#### Explanation:

color(blue)(3/4x-6=1/2x-9

$\rightarrow \frac{3 \cdot x}{4} - 6 = \frac{x \cdot 1}{2} - 9$

$\rightarrow \frac{3 x}{4} - 6 = \frac{x}{2} - 9$

Add $6$ both sides

$\rightarrow \frac{3 x}{4} \cancel{- 6 \textcolor{p e r p \le}{+ 6}} = \frac{x}{2} - 9 \textcolor{p u r p \le}{+ 6}$

$\rightarrow \frac{3 x}{4} = \frac{x}{2} - 3$

Subtract $\frac{x}{2}$ both sides

rarr(3x)/(4)-color(purple)(x/2)=cancel(x/2)-3-cancel(color(purple)(x/2

By subtracting the fractions

$\rightarrow \frac{3 x - 2 x}{4} = - 3$

$\rightarrow \frac{x}{4} = - 3$

Multiply both sides by $4$

$\rightarrow \frac{x}{\cancel{4}} \cdot \cancel{\textcolor{p u r p \le}{4}} = - 3 \cdot \textcolor{p u r p \le}{4}$

color(green)(rArrx=-12