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

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

Solve for a

$$a=\frac{7}{9}\approx 0.777777778$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 2,3.

$$6a-3\left(a-1\right)=6-6\left(a-\frac{2}{3}\right)$$

Use the distributive property to multiply -3 by a-1.

$$6a-3a+3=6-6\left(a-\frac{2}{3}\right)$$

Combine 6a and -3a to get 3a.

$$3a+3=6-6\left(a-\frac{2}{3}\right)$$

Use the distributive property to multiply -6 by a-\frac{2}{3}.

$$3a+3=6-6a-6\left(-\frac{2}{3}\right)$$

Express -6\left(-\frac{2}{3}\right) as a single fraction.

$$3a+3=6-6a+\frac{-6\left(-2\right)}{3}$$

Multiply -6 and -2 to get 12.

$$3a+3=6-6a+\frac{12}{3}$$

Divide 12 by 3 to get 4.

$$3a+3=6-6a+4$$

Add 6 and 4 to get 10.

$$3a+3=10-6a$$

Add 6a to both sides.

$$3a+3+6a=10$$

Combine 3a and 6a to get 9a.

$$9a+3=10$$

Subtract 3 from both sides.

$$9a=10-3$$

Subtract 3 from 10 to get 7.

$$9a=7$$

Divide both sides by 9.

$$a=\frac{7}{9}$$