Solve 4-2/3(x-1)=x-2

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

Solve for x

$$x=4$$

Steps for Solving Linear Equation

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

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

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

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

Convert 4 to fraction \frac{12}{3}.

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

Since \frac{12}{3} and \frac{2}{3} have the same denominator, add them by adding their numerators.

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

Add 12 and 2 to get 14.

$$\frac{14}{3}-\frac{2}{3}x=x-2$$

Subtract x from both sides.

$$\frac{14}{3}-\frac{2}{3}x-x=-2$$

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

$$\frac{14}{3}-\frac{5}{3}x=-2$$

Subtract \frac{14}{3} from both sides.

$$-\frac{5}{3}x=-2-\frac{14}{3}$$

Convert -2 to fraction -\frac{6}{3}.

$$-\frac{5}{3}x=-\frac{6}{3}-\frac{14}{3}$$

Since -\frac{6}{3} and \frac{14}{3} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{5}{3}x=\frac{-6-14}{3}$$

Subtract 14 from -6 to get -20.

$$-\frac{5}{3}x=-\frac{20}{3}$$

Multiply both sides by -\frac{3}{5}, the reciprocal of -\frac{5}{3}.

$$x=-\frac{20}{3}\left(-\frac{3}{5}\right)$$

Multiply -\frac{20}{3} times -\frac{3}{5} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{-20\left(-3\right)}{3\times 5}$$

Do the multiplications in the fraction \frac{-20\left(-3\right)}{3\times 5}.

$$x=\frac{60}{15}$$

Divide 60 by 15 to get 4.

$$x=4$$