Solve 4/10x-3x+8/5=4/5

$$\frac { 4 } { 10 } x - 3 x + \frac { 8 } { 5 } = \frac { 4 } { 5 }$$

Solve for x

$$x=\frac{4}{13}\approx 0.307692308$$

Steps for Solving Linear Equation

Reduce the fraction \frac{4}{10} to lowest terms by extracting and canceling out 2.

$$\frac{2}{5}x-3x+\frac{8}{5}=\frac{4}{5}$$

Combine \frac{2}{5}x and -3x to get -\frac{13}{5}x.

$$-\frac{13}{5}x+\frac{8}{5}=\frac{4}{5}$$

Subtract \frac{8}{5} from both sides.

$$-\frac{13}{5}x=\frac{4}{5}-\frac{8}{5}$$

Since \frac{4}{5} and \frac{8}{5} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{13}{5}x=\frac{4-8}{5}$$

Subtract 8 from 4 to get -4.

$$-\frac{13}{5}x=-\frac{4}{5}$$

Multiply both sides by -\frac{5}{13}, the reciprocal of -\frac{13}{5}.

$$x=-\frac{4}{5}\left(-\frac{5}{13}\right)$$

Multiply -\frac{4}{5} times -\frac{5}{13} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-4\left(-5\right)}{5\times 13}$$

Do the multiplications in the fraction \frac{-4\left(-5\right)}{5\times 13}.

$$x=\frac{20}{65}$$

Reduce the fraction \frac{20}{65} to lowest terms by extracting and canceling out 5.

$$x=\frac{4}{13}$$