Solve 2/3left(x-1-x-2/3right)+1=x

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

Solve for x

$$x = \frac{7}{5} = 1\frac{2}{5} = 1.4$$

Steps for Solving Linear Equation

Use the distributive property to multiply \frac{2}{3} by x-1-\frac{x-2}{3}.

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

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

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

Multiply \frac{2}{3} times -\frac{x-2}{3} by multiplying numerator times numerator and denominator times denominator.

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

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

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

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

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

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

$$\frac{2}{3}x+\frac{-6-2x+4}{3\times 3}+1=x$$

Combine like terms in -6-2x+4.

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

Multiply 3 and 3 to get 9.

$$\frac{2}{3}x+\frac{-2-2x}{9}+1=x$$

Divide each term of -2-2x by 9 to get -\frac{2}{9}-\frac{2}{9}x.

$$\frac{2}{3}x-\frac{2}{9}-\frac{2}{9}x+1=x$$

Combine \frac{2}{3}x and -\frac{2}{9}x to get \frac{4}{9}x.

$$\frac{4}{9}x-\frac{2}{9}+1=x$$

Convert 1 to fraction \frac{9}{9}.

$$\frac{4}{9}x-\frac{2}{9}+\frac{9}{9}=x$$

Since -\frac{2}{9} and \frac{9}{9} have the same denominator, add them by adding their numerators.

$$\frac{4}{9}x+\frac{-2+9}{9}=x$$

Add -2 and 9 to get 7.

$$\frac{4}{9}x+\frac{7}{9}=x$$

Subtract x from both sides.

$$\frac{4}{9}x+\frac{7}{9}-x=0$$

Combine \frac{4}{9}x and -x to get -\frac{5}{9}x.

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

Subtract \frac{7}{9} from both sides. Anything subtracted from zero gives its negation.

$$-\frac{5}{9}x=-\frac{7}{9}$$

Multiply both sides by -\frac{9}{5}, the reciprocal of -\frac{5}{9}.

$$x=-\frac{7}{9}\left(-\frac{9}{5}\right)$$

Multiply -\frac{7}{9} times -\frac{9}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-7\left(-9\right)}{9\times 5}$$

Do the multiplications in the fraction \frac{-7\left(-9\right)}{9\times 5}.

$$x=\frac{63}{45}$$

Reduce the fraction \frac{63}{45} to lowest terms by extracting and canceling out 9.

$$x=\frac{7}{5}$$