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

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

Solve for x

$$x = \frac{11}{5} = 2\frac{1}{5} = 2.2$$

Steps for Solving Linear Equation

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

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

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

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

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

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

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

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

Multiply \frac{1}{2} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

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

Do the multiplications in the fraction \frac{1\times 1}{2\times 2}.

$$\frac{1}{4}x+\frac{1}{2}\times \frac{1}{2}=\frac{2}{3}\left(x-1\right)$$

Multiply \frac{1}{2} times \frac{1}{2} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{4}x+\frac{1\times 1}{2\times 2}=\frac{2}{3}\left(x-1\right)$$

Do the multiplications in the fraction \frac{1\times 1}{2\times 2}.

$$\frac{1}{4}x+\frac{1}{4}=\frac{2}{3}\left(x-1\right)$$

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

$$\frac{1}{4}x+\frac{1}{4}=\frac{2}{3}x+\frac{2}{3}\left(-1\right)$$

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

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

Subtract \frac{2}{3}x from both sides.

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

Combine \frac{1}{4}x and -\frac{2}{3}x to get -\frac{5}{12}x.

$$-\frac{5}{12}x+\frac{1}{4}=-\frac{2}{3}$$

Subtract \frac{1}{4} from both sides.

$$-\frac{5}{12}x=-\frac{2}{3}-\frac{1}{4}$$

Least common multiple of 3 and 4 is 12. Convert -\frac{2}{3} and \frac{1}{4} to fractions with denominator 12.

$$-\frac{5}{12}x=-\frac{8}{12}-\frac{3}{12}$$

Since -\frac{8}{12} and \frac{3}{12} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{5}{12}x=\frac{-8-3}{12}$$

Subtract 3 from -8 to get -11.

$$-\frac{5}{12}x=-\frac{11}{12}$$

Multiply both sides by -\frac{12}{5}, the reciprocal of -\frac{5}{12}.

$$x=-\frac{11}{12}\left(-\frac{12}{5}\right)$$

Multiply -\frac{11}{12} times -\frac{12}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-11\left(-12\right)}{12\times 5}$$

Do the multiplications in the fraction \frac{-11\left(-12\right)}{12\times 5}.

$$x=\frac{132}{60}$$

Reduce the fraction \frac{132}{60} to lowest terms by extracting and canceling out 12.

$$x=\frac{11}{5}$$