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

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

Solve for x

$$x=14$$

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{x+4}{2} times \frac{5}{5}.

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

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

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

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

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

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

$$\frac{9x+14}{10}=x$$

Divide each term of 9x+14 by 10 to get \frac{9}{10}x+\frac{7}{5}.

$$\frac{9}{10}x+\frac{7}{5}=x$$

Subtract x from both sides.

$$\frac{9}{10}x+\frac{7}{5}-x=0$$

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

$$-\frac{1}{10}x+\frac{7}{5}=0$$

Subtract \frac{7}{5} from both sides. Anything subtracted from zero gives its negation.

$$-\frac{1}{10}x=-\frac{7}{5}$$

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

$$x=-\frac{7}{5}\left(-10\right)$$

Express -\frac{7}{5}\left(-10\right) as a single fraction.

$$x=\frac{-7\left(-10\right)}{5}$$

Multiply -7 and -10 to get 70.

$$x=\frac{70}{5}$$

Divide 70 by 5 to get 14.

$$x=14$$