Solve 0.5(x-0.5(x-1))=2/3(x-1)

$$0.5(x-0.5(x-1))= \frac{ 2 }{ 3 } (x-1)$$

Solve for x

$$x=2.2$$

Steps for Solving Linear Equation

Use the distributive property to multiply -0.5 by x-1.

$$0.5\left(x-0.5x+0.5\right)=\frac{2}{3}\left(x-1\right)$$

Combine x and -0.5x to get 0.5x.

$$0.5\left(0.5x+0.5\right)=\frac{2}{3}\left(x-1\right)$$

Use the distributive property to multiply 0.5 by 0.5x+0.5.

$$0.25x+0.25=\frac{2}{3}\left(x-1\right)$$

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

$$0.25x+0.25=\frac{2}{3}x+\frac{2}{3}\left(-1\right)$$

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

$$0.25x+0.25=\frac{2}{3}x-\frac{2}{3}$$

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

$$0.25x+0.25-\frac{2}{3}x=-\frac{2}{3}$$

Combine 0.25x and -\frac{2}{3}x to get -\frac{5}{12}x.

$$-\frac{5}{12}x+0.25=-\frac{2}{3}$$

Subtract 0.25 from both sides.

$$-\frac{5}{12}x=-\frac{2}{3}-0.25$$

Convert decimal number 0.25 to fraction \frac{25}{100}. Reduce the fraction \frac{25}{100} to lowest terms by extracting and canceling out 25.

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

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.

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