Solve 2/5-x=1/2x+4/5

$$\frac { 2 } { 5 } - x = \frac { 1 } { 2 } x + \frac { 4 } { 5 }$$

Solve for x

$$x=-\frac{4}{15}\approx -0.266666667$$

Steps for Solving Linear Equation

Subtract \frac{1}{2}x from both sides.

$$\frac{2}{5}-x-\frac{1}{2}x=\frac{4}{5}$$

Combine -x and -\frac{1}{2}x to get -\frac{3}{2}x.

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

Subtract \frac{2}{5} from both sides.

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

Since \frac{4}{5} and \frac{2}{5} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 2 from 4 to get 2.

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

Multiply both sides by -\frac{2}{3}, the reciprocal of -\frac{3}{2}.

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

Multiply \frac{2}{5} times -\frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{2\left(-2\right)}{5\times 3}.

$$x=\frac{-4}{15}$$

Fraction \frac{-4}{15} can be rewritten as -\frac{4}{15} by extracting the negative sign.

$$x=-\frac{4}{15}$$