Solve 2-1/3(a-1)=2

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

Solve for a

$$a=1$$

Steps for Solving Linear Equation

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

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

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

$$2-\frac{1}{3}a+\frac{1}{3}=2$$

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

$$\frac{6}{3}-\frac{1}{3}a+\frac{1}{3}=2$$

Since \frac{6}{3} and \frac{1}{3} have the same denominator, add them by adding their numerators.

$$\frac{6+1}{3}-\frac{1}{3}a=2$$

Add 6 and 1 to get 7.

$$\frac{7}{3}-\frac{1}{3}a=2$$

Subtract \frac{7}{3} from both sides.

$$-\frac{1}{3}a=2-\frac{7}{3}$$

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

$$-\frac{1}{3}a=\frac{6}{3}-\frac{7}{3}$$

Since \frac{6}{3} and \frac{7}{3} have the same denominator, subtract them by subtracting their numerators.

$$-\frac{1}{3}a=\frac{6-7}{3}$$

Subtract 7 from 6 to get -1.

$$-\frac{1}{3}a=-\frac{1}{3}$$

Multiply both sides by -3, the reciprocal of -\frac{1}{3}.

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

Express -\frac{1}{3}\left(-3\right) as a single fraction.

$$a=\frac{-\left(-3\right)}{3}$$

Multiply -1 and -3 to get 3.

$$a=\frac{3}{3}$$

Divide 3 by 3 to get 1.

$$a=1$$