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

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

Solve for x

$$x = -\frac{18}{17} = -1\frac{1}{17} \approx -1.058823529$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 3.

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

Combine x and -\frac{x}{2} to get \frac{1}{2}x.

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

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

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

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

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

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

$$-3\left(\frac{5}{2}x+6-3\right)=x$$

Subtract 3 from 6 to get 3.

$$-3\left(\frac{5}{2}x+3\right)=x$$

Use the distributive property to multiply -3 by \frac{5}{2}x+3.

$$-3\times \frac{5}{2}x-9=x$$

Express -3\times \frac{5}{2} as a single fraction.

$$\frac{-3\times 5}{2}x-9=x$$

Multiply -3 and 5 to get -15.

$$\frac{-15}{2}x-9=x$$

Fraction \frac{-15}{2} can be rewritten as -\frac{15}{2} by extracting the negative sign.

$$-\frac{15}{2}x-9=x$$

Subtract x from both sides.

$$-\frac{15}{2}x-9-x=0$$

Combine -\frac{15}{2}x and -x to get -\frac{17}{2}x.

$$-\frac{17}{2}x-9=0$$

Add 9 to both sides. Anything plus zero gives itself.

$$-\frac{17}{2}x=9$$

Multiply both sides by -\frac{2}{17}, the reciprocal of -\frac{17}{2}.

$$x=9\left(-\frac{2}{17}\right)$$

Express 9\left(-\frac{2}{17}\right) as a single fraction.

$$x=\frac{9\left(-2\right)}{17}$$

Multiply 9 and -2 to get -18.

$$x=\frac{-18}{17}$$

Fraction \frac{-18}{17} can be rewritten as -\frac{18}{17} by extracting the negative sign.

$$x=-\frac{18}{17}$$