Solve 1+3/5(x-5/3)=2x-1/5

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

Solve for x

$$x=\frac{1}{7}\approx 0.142857143$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{3}{5} by x-\frac{5}{3}.

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

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

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

Cancel out 3 in both numerator and denominator.

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

Divide -5 by 5 to get -1.

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

Subtract 1 from 1 to get 0.

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

Subtract 2x from both sides.

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

Combine \frac{3}{5}x and -2x to get -\frac{7}{5}x.

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

Multiply both sides by -\frac{5}{7}, the reciprocal of -\frac{7}{5}.

$$x=-\frac{1}{5}\left(-\frac{5}{7}\right)$$

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

$$x=\frac{-\left(-5\right)}{5\times 7}$$

Do the multiplications in the fraction \frac{-\left(-5\right)}{5\times 7}.

$$x=\frac{5}{35}$$

Reduce the fraction \frac{5}{35} to lowest terms by extracting and canceling out 5.

$$x=\frac{1}{7}$$