Solve 5x-1/2+x+1/3=x

$$\frac{ 5x-1 }{ 2 } + \frac{ x+1 }{ 3 } = x$$

Solve for x

$$x=\frac{1}{11}\approx 0.090909091$$

Steps for Solving Linear Equation

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 2 and 3 is 6. Multiply \frac{5x-1}{2} times \frac{3}{3}. Multiply \frac{x+1}{3} times \frac{2}{2}.

$$\frac{3\left(5x-1\right)}{6}+\frac{2\left(x+1\right)}{6}=x$$

Since \frac{3\left(5x-1\right)}{6} and \frac{2\left(x+1\right)}{6} have the same denominator, add them by adding their numerators.

$$\frac{3\left(5x-1\right)+2\left(x+1\right)}{6}=x$$

Do the multiplications in 3\left(5x-1\right)+2\left(x+1\right).

$$\frac{15x-3+2x+2}{6}=x$$

Combine like terms in 15x-3+2x+2.

$$\frac{17x-1}{6}=x$$

Divide each term of 17x-1 by 6 to get \frac{17}{6}x-\frac{1}{6}.

$$\frac{17}{6}x-\frac{1}{6}=x$$

Subtract x from both sides.

$$\frac{17}{6}x-\frac{1}{6}-x=0$$

Combine \frac{17}{6}x and -x to get \frac{11}{6}x.

$$\frac{11}{6}x-\frac{1}{6}=0$$

Add \frac{1}{6} to both sides. Anything plus zero gives itself.

$$\frac{11}{6}x=\frac{1}{6}$$

Multiply both sides by \frac{6}{11}, the reciprocal of \frac{11}{6}.

$$x=\frac{1}{6}\times \frac{6}{11}$$

Multiply \frac{1}{6} times \frac{6}{11} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{1\times 6}{6\times 11}$$

Cancel out 6 in both numerator and denominator.

$$x=\frac{1}{11}$$