# How do you solve 1/3(9x-2) = 1/2(8x-6)?

Apr 10, 2016

$x = \frac{7}{3}$

#### Explanation:

color(blue)(1/3(9x-2)=1/2(8x-6)

Use distributive property

color(brown)(a(b+c)=ab+ac

$\rightarrow \left(\frac{1}{3} \cdot 9 x\right) - \left(\frac{1}{3} \cdot 2\right) = \left(\frac{1}{2} \cdot 8 x\right) - \left(\frac{1}{2} \cdot 6\right)$

Remove the brackets and solve

$\rightarrow \frac{1}{\cancel{3}} ^ 1 \cdot {\cancel{9}}^{3} x - \frac{1}{3} \cdot 2 = \frac{1}{\cancel{2}} ^ 1 \cdot {\cancel{8}}^{4} x - \frac{1}{\cancel{2}} ^ 1 \cdot {\cancel{6}}^{3}$

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

Subtract $3 x$ both sides

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

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

Add $3$ both sides

rarr-2/3+3=xcancel(-3+3

color(green)(rArrx=7/3

Apr 10, 2016

$x = \frac{7}{3}$

#### Explanation:

$1$. Start by factoring out $2$ from $\left(8 x - 6\right)$.

$\frac{1}{3} \left(9 x - 2\right) = \frac{1}{2} \left(8 x - 6\right)$

$\frac{1}{3} \left(9 x - 2\right) = \frac{1}{2} \cdot 2 \left(4 x - 3\right)$

$2$. Simplify the right side of the equation.

$\frac{1}{3} \left(9 x - 2\right) = \left(4 x - 3\right)$

$3$. Multiply both sides of the equation by $3$ to get rid of the denominator.

$\textcolor{red}{3} \left[\frac{1}{3} \left(9 x - 2\right)\right] = \textcolor{red}{3} \left(4 x - 3\right)$

$4$. Simplify the left side of the equation.

$9 x - 2 = 3 \left(4 x - 3\right)$

$5$. Expand the bracket.

$9 x - 2 = 12 x - 9$

$6$. Solve for $x$.

$3 x = 7$

$\textcolor{g r e e n}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} x = \frac{7}{3} \textcolor{w h i t e}{\frac{a}{a}} |}}}$