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

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

Solve for x

$$x=\frac{2}{3}\approx 0.666666667$$

Steps for Solving Linear Equation

Convert -1 to fraction -\frac{3}{3}.

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

Since -\frac{3}{3} and \frac{2}{3} have the same denominator, add them by adding their numerators.

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

Add -3 and 2 to get -1.

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

Subtract x from both sides.

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

Combine -x and -x to get -2x.

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

Subtract 1 from both sides.

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

Convert 1 to fraction \frac{3}{3}.

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

Since -\frac{1}{3} and \frac{3}{3} have the same denominator, subtract them by subtracting their numerators.

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

Subtract 3 from -1 to get -4.

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

Divide both sides by -2.

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

Express \frac{-\frac{4}{3}}{-2} as a single fraction.

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

Multiply 3 and -2 to get -6.

$$x=\frac{-4}{-6}$$

Reduce the fraction \frac{-4}{-6} to lowest terms by extracting and canceling out -2.

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