Solve 2x-1/2[x-1/2(x-1)]=2/3(x-1)

$$2 x - \frac { 1 } { 2 } [ x - \frac { 1 } { 2 } ( x - 1 ) ] = \frac { 2 } { 3 } ( x - 1 )$$

Solve for x

$$x=-\frac{5}{13}\approx -0.384615385$$

Steps for Solving Linear Equation

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

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

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

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

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

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

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

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

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

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

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

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

Fraction \frac{-1}{4} can be rewritten as -\frac{1}{4} by extracting the negative sign.

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

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

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

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

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

Fraction \frac{-1}{4} can be rewritten as -\frac{1}{4} by extracting the negative sign.

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

Combine 2x and -\frac{1}{4}x to get \frac{7}{4}x.

$$\frac{7}{4}x-\frac{1}{4}=\frac{2}{3}\left(x-1\right)$$

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

$$\frac{7}{4}x-\frac{1}{4}=\frac{2}{3}x+\frac{2}{3}\left(-1\right)$$

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

$$\frac{7}{4}x-\frac{1}{4}=\frac{2}{3}x-\frac{2}{3}$$

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

$$\frac{7}{4}x-\frac{1}{4}-\frac{2}{3}x=-\frac{2}{3}$$

Combine \frac{7}{4}x and -\frac{2}{3}x to get \frac{13}{12}x.

$$\frac{13}{12}x-\frac{1}{4}=-\frac{2}{3}$$

Add \frac{1}{4} to both sides.

$$\frac{13}{12}x=-\frac{2}{3}+\frac{1}{4}$$

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

$$\frac{13}{12}x=-\frac{8}{12}+\frac{3}{12}$$

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

$$\frac{13}{12}x=\frac{-8+3}{12}$$

Add -8 and 3 to get -5.

$$\frac{13}{12}x=-\frac{5}{12}$$

Multiply both sides by \frac{12}{13}, the reciprocal of \frac{13}{12}.

$$x=-\frac{5}{12}\times \frac{12}{13}$$

Multiply -\frac{5}{12} times \frac{12}{13} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-5\times 12}{12\times 13}$$

Cancel out 12 in both numerator and denominator.

$$x=\frac{-5}{13}$$

Fraction \frac{-5}{13} can be rewritten as -\frac{5}{13} by extracting the negative sign.

$$x=-\frac{5}{13}$$