Solve 3(3x-1)=2(3x+2)(R:7/3)

$$3 ( 3 x - 1 ) = 2 ( 3 x + 2 ) ( R : 7 / 3 )$$

Solve for x

$$x=\frac{4R+7}{3\left(7-2R\right)}$$

$$R\neq \frac{7}{2}$$

Steps for Solving Linear Equation

Use the distributive property to multiply 3 by 3x-1.

$$9x-3=2\left(3x+2\right)\times \frac{R}{\frac{7}{3}}$$

Use the distributive property to multiply 2 by 3x+2.

$$9x-3=\left(6x+4\right)\times \frac{R}{\frac{7}{3}}$$

Use the distributive property to multiply 6x+4 by \frac{R}{\frac{7}{3}}.

$$9x-3=6x\times \frac{R}{\frac{7}{3}}+4\times \frac{R}{\frac{7}{3}}$$

Subtract 6x\times \frac{R}{\frac{7}{3}} from both sides.

$$9x-3-6x\times \frac{R}{\frac{7}{3}}=4\times \frac{R}{\frac{7}{3}}$$

Add 3 to both sides.

$$9x-6x\times \frac{R}{\frac{7}{3}}=4\times \frac{R}{\frac{7}{3}}+3$$

Combine all terms containing x.

$$\left(9-6\times \frac{R}{\frac{7}{3}}\right)x=4\times \frac{R}{\frac{7}{3}}+3$$

The equation is in standard form.

$$\left(-\frac{18R}{7}+9\right)x=\frac{12R}{7}+3$$

Divide both sides by 9-\frac{18}{7}R.

$$\frac{\left(-\frac{18R}{7}+9\right)x}{-\frac{18R}{7}+9}=\frac{\frac{12R}{7}+3}{-\frac{18R}{7}+9}$$

Dividing by 9-\frac{18}{7}R undoes the multiplication by 9-\frac{18}{7}R.

$$x=\frac{\frac{12R}{7}+3}{-\frac{18R}{7}+9}$$

Divide \frac{12R}{7}+3 by 9-\frac{18}{7}R.

$$x=\frac{4R+7}{3\left(7-2R\right)}$$

Solve for R

$$R=-\frac{7\left(1-3x\right)}{2\left(3x+2\right)}$$

$$x\neq -\frac{2}{3}$$