Solve -{-1/2[-1+1/3(x-9)]-x+3/3}=x-1/2-frac{x-1}{3}

$$- \{ - \frac { 1 } { 2 } [ - 1 + \frac { 1 } { 3 } ( x - 9 ) ] - \frac { x + 3 } { 3 } \} = x - \frac { 1 } { 2 } - \frac { x - 1 } { 3 }$$

Solve for x

$$x=-5$$

Steps for Solving Linear Equation

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

$$-6\left(-\frac{1}{2}\left(-1+\frac{1}{3}\left(x-9\right)\right)-\frac{x+3}{3}\right)=6x-3-2\left(x-1\right)$$

Use the distributive property to multiply \frac{1}{3} by x-9.

$$-6\left(-\frac{1}{2}\left(-1+\frac{1}{3}x+\frac{1}{3}\left(-9\right)\right)-\frac{x+3}{3}\right)=6x-3-2\left(x-1\right)$$

Multiply \frac{1}{3} and -9 to get \frac{-9}{3}.

$$-6\left(-\frac{1}{2}\left(-1+\frac{1}{3}x+\frac{-9}{3}\right)-\frac{x+3}{3}\right)=6x-3-2\left(x-1\right)$$

Divide -9 by 3 to get -3.

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

Subtract 3 from -1 to get -4.

$$-6\left(-\frac{1}{2}\left(-4+\frac{1}{3}x\right)-\frac{x+3}{3}\right)=6x-3-2\left(x-1\right)$$

Use the distributive property to multiply -\frac{1}{2} by -4+\frac{1}{3}x.

$$-6\left(-\frac{1}{2}\left(-4\right)-\frac{1}{2}\times \frac{1}{3}x-\frac{x+3}{3}\right)=6x-3-2\left(x-1\right)$$

Express -\frac{1}{2}\left(-4\right) as a single fraction.

$$-6\left(\frac{-\left(-4\right)}{2}-\frac{1}{2}\times \frac{1}{3}x-\frac{x+3}{3}\right)=6x-3-2\left(x-1\right)$$

Multiply -1 and -4 to get 4.

$$-6\left(\frac{4}{2}-\frac{1}{2}\times \frac{1}{3}x-\frac{x+3}{3}\right)=6x-3-2\left(x-1\right)$$

Divide 4 by 2 to get 2.

$$-6\left(2-\frac{1}{2}\times \frac{1}{3}x-\frac{x+3}{3}\right)=6x-3-2\left(x-1\right)$$

Multiply -\frac{1}{2} times \frac{1}{3} by multiplying numerator times numerator and denominator times denominator.

$$-6\left(2+\frac{-1}{2\times 3}x-\frac{x+3}{3}\right)=6x-3-2\left(x-1\right)$$

Do the multiplications in the fraction \frac{-1}{2\times 3}.

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

Fraction \frac{-1}{6} can be rewritten as -\frac{1}{6} by extracting the negative sign.

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

Use the distributive property to multiply -6 by 2-\frac{1}{6}x-\frac{x+3}{3}.

$$-12-6\left(-\frac{1}{6}\right)x-6\left(-\frac{x+3}{3}\right)=6x-3-2\left(x-1\right)$$

Multiply -6 times -\frac{1}{6}.

$$-12+x-6\left(-\frac{x+3}{3}\right)=6x-3-2\left(x-1\right)$$

Multiply -6 and -1 to get 6.

$$-12+x+6\times \frac{x+3}{3}=6x-3-2\left(x-1\right)$$

Cancel out 3, the greatest common factor in 6 and 3.

$$-12+x+2\left(x+3\right)=6x-3-2\left(x-1\right)$$

Use the distributive property to multiply 2 by x+3.

$$-12+x+2x+6=6x-3-2\left(x-1\right)$$

Combine x and 2x to get 3x.

$$-12+3x+6=6x-3-2\left(x-1\right)$$

Add -12 and 6 to get -6.

$$-6+3x=6x-3-2\left(x-1\right)$$

Use the distributive property to multiply -2 by x-1.

$$-6+3x=6x-3-2x+2$$

Combine 6x and -2x to get 4x.

$$-6+3x=4x-3+2$$

Add -3 and 2 to get -1.

$$-6+3x=4x-1$$

Subtract 4x from both sides.

$$-6+3x-4x=-1$$

Combine 3x and -4x to get -x.

$$-6-x=-1$$

Add 6 to both sides.

$$-x=-1+6$$

Add -1 and 6 to get 5.

$$-x=5$$

Multiply both sides by -1.

$$x=-5$$