Solve (X+1)/2+(X-1)/6=X

$$( X + 1 ) / 2 + ( X - 1 ) / 6 = X$$

Solve for X

$$X=1$$

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 6 is 6. Multiply \frac{X+1}{2} times \frac{3}{3}.

$$\frac{3\left(X+1\right)}{6}+\frac{X-1}{6}=X$$

Since \frac{3\left(X+1\right)}{6} and \frac{X-1}{6} have the same denominator, add them by adding their numerators.

$$\frac{3\left(X+1\right)+X-1}{6}=X$$

Do the multiplications in 3\left(X+1\right)+X-1.

$$\frac{3X+3+X-1}{6}=X$$

Combine like terms in 3X+3+X-1.

$$\frac{4X+2}{6}=X$$

Divide each term of 4X+2 by 6 to get \frac{2}{3}X+\frac{1}{3}.

$$\frac{2}{3}X+\frac{1}{3}=X$$

Subtract X from both sides.

$$\frac{2}{3}X+\frac{1}{3}-X=0$$

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

$$-\frac{1}{3}X+\frac{1}{3}=0$$

Subtract \frac{1}{3} from both sides. Anything subtracted from zero gives its negation.

$$-\frac{1}{3}X=-\frac{1}{3}$$

Multiply both sides by -3, the reciprocal of -\frac{1}{3}.

$$X=-\frac{1}{3}\left(-3\right)$$

Express -\frac{1}{3}\left(-3\right) as a single fraction.

$$X=\frac{-\left(-3\right)}{3}$$

Multiply -1 and -3 to get 3.

$$X=\frac{3}{3}$$

Divide 3 by 3 to get 1.

$$X=1$$