Solve 3x-1/7:3/5=2x/3:7/5

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

Solve for x

$$x=1$$

Steps for Solving Linear Equation

Divide each term of 3x-1 by 7 to get \frac{3}{7}x-\frac{1}{7}.

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

Divide each term of \frac{3}{7}x-\frac{1}{7} by \frac{3}{5} to get \frac{\frac{3}{7}x}{\frac{3}{5}}+\frac{-\frac{1}{7}}{\frac{3}{5}}.

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

Divide \frac{3}{7}x by \frac{3}{5} to get \frac{5}{7}x.

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

Divide -\frac{1}{7} by \frac{3}{5} by multiplying -\frac{1}{7} by the reciprocal of \frac{3}{5}.

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

Multiply -\frac{1}{7} times \frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{-5}{7\times 3}.

$$\frac{5}{7}x+\frac{-5}{21}=\frac{\frac{2x}{3}}{\frac{7}{5}}$$

Fraction \frac{-5}{21} can be rewritten as -\frac{5}{21} by extracting the negative sign.

$$\frac{5}{7}x-\frac{5}{21}=\frac{\frac{2x}{3}}{\frac{7}{5}}$$

Subtract \frac{\frac{2x}{3}}{\frac{7}{5}} from both sides.

$$\frac{5}{7}x-\frac{5}{21}-\frac{\frac{2x}{3}}{\frac{7}{5}}=0$$

Add \frac{5}{21} to both sides. Anything plus zero gives itself.

$$\frac{5}{7}x-\frac{\frac{2x}{3}}{\frac{7}{5}}=\frac{5}{21}$$

Reorder the terms.

$$-\frac{2x}{\frac{7}{5}\times 3}+\frac{5}{7}x=\frac{5}{21}$$

Express \frac{7}{5}\times 3 as a single fraction.

$$-\frac{2x}{\frac{7\times 3}{5}}+\frac{5}{7}x=\frac{5}{21}$$

Multiply 7 and 3 to get 21.

$$-\frac{2x}{\frac{21}{5}}+\frac{5}{7}x=\frac{5}{21}$$

Divide 2x by \frac{21}{5} to get \frac{10}{21}x.

$$-\frac{10}{21}x+\frac{5}{7}x=\frac{5}{21}$$

Combine -\frac{10}{21}x and \frac{5}{7}x to get \frac{5}{21}x.

$$\frac{5}{21}x=\frac{5}{21}$$

Multiply both sides by \frac{21}{5}, the reciprocal of \frac{5}{21}.

$$x=\frac{5}{21}\times \frac{21}{5}$$

Cancel out \frac{5}{21} and its reciprocal \frac{21}{5}.

$$x=1$$