Solve 2x-3/5-4-x/2=x

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

Solve for x

$$x=-26$$

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 5 and 2 is 10. Multiply \frac{2x-3}{5} times \frac{2}{2}. Multiply \frac{4-x}{2} times \frac{5}{5}.

$$\frac{2\left(2x-3\right)}{10}-\frac{5\left(4-x\right)}{10}=x$$

Since \frac{2\left(2x-3\right)}{10} and \frac{5\left(4-x\right)}{10} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2\left(2x-3\right)-5\left(4-x\right)}{10}=x$$

Do the multiplications in 2\left(2x-3\right)-5\left(4-x\right).

$$\frac{4x-6-20+5x}{10}=x$$

Combine like terms in 4x-6-20+5x.

$$\frac{9x-26}{10}=x$$

Divide each term of 9x-26 by 10 to get \frac{9}{10}x-\frac{13}{5}.

$$\frac{9}{10}x-\frac{13}{5}=x$$

Subtract x from both sides.

$$\frac{9}{10}x-\frac{13}{5}-x=0$$

Combine \frac{9}{10}x and -x to get -\frac{1}{10}x.

$$-\frac{1}{10}x-\frac{13}{5}=0$$

Add \frac{13}{5} to both sides. Anything plus zero gives itself.

$$-\frac{1}{10}x=\frac{13}{5}$$

Multiply both sides by -10, the reciprocal of -\frac{1}{10}.

$$x=\frac{13}{5}\left(-10\right)$$

Express \frac{13}{5}\left(-10\right) as a single fraction.

$$x=\frac{13\left(-10\right)}{5}$$

Multiply 13 and -10 to get -130.

$$x=\frac{-130}{5}$$

Divide -130 by 5 to get -26.

$$x=-26$$