Solve (text{(vii)})2/5x+3/frac{7{3}x-1}=3/5

$$( \text { (vii) } ) \frac { \frac { 2 } { 5 } x + 3 } { \frac { 7 } { 3 } x - 1 } = \frac { 3 } { 5 }$$

Solve for v

$$v=\frac{3-7x}{2x+15}$$

$$x\neq -\frac{15}{2}\text{ and }x\neq \frac{3}{7}$$

Steps for Solving Linear Equation

Multiply i and i to get -1.

$$v\left(-1\right)\times \frac{\frac{2}{5}x+3}{\frac{7}{3}x-1}=\frac{3}{5}$$

The equation is in standard form.

$$\left(-\frac{\frac{2x}{5}+3}{\frac{7x}{3}-1}\right)v=\frac{3}{5}$$

Divide both sides by -\left(\frac{2}{5}x+3\right)\left(\frac{7}{3}x-1\right)^{-1}.

$$\frac{\left(-\frac{\frac{2x}{5}+3}{\frac{7x}{3}-1}\right)v}{-\frac{\frac{2x}{5}+3}{\frac{7x}{3}-1}}=\frac{\frac{3}{5}}{-\frac{\frac{2x}{5}+3}{\frac{7x}{3}-1}}$$

Dividing by -\left(\frac{2}{5}x+3\right)\left(\frac{7}{3}x-1\right)^{-1} undoes the multiplication by -\left(\frac{2}{5}x+3\right)\left(\frac{7}{3}x-1\right)^{-1}.

$$v=\frac{\frac{3}{5}}{-\frac{\frac{2x}{5}+3}{\frac{7x}{3}-1}}$$

Divide \frac{3}{5} by -\left(\frac{2}{5}x+3\right)\left(\frac{7}{3}x-1\right)^{-1}.

$$v=-\frac{7x-3}{2x+15}$$

Solve for x

$$x=-\frac{3\left(5v-1\right)}{2v+7}$$

$$v\neq 0\text{ and }v\neq -\frac{7}{2}$$