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

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

Solve for x

$$x=-2$$

Steps for Solving Linear Equation

To find the opposite of -x-2, find the opposite of each term.

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

The opposite of -2 is 2.

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

Add 3 and 2 to get 5.

$$x+x+3-\left(x+5-\left(-x\right)\right)=x$$

To find the opposite of x+5-\left(-x\right), find the opposite of each term.

$$x+x+3-x-5-\left(-\left(-x\right)\right)=x$$

Combine x and -x to get 0.

$$x+3-5-\left(-\left(-x\right)\right)=x$$

Subtract 5 from 3 to get -2.

$$x-2-\left(-\left(-x\right)\right)=x$$

Subtract x from both sides.

$$x-2-\left(-\left(-x\right)\right)-x=0$$

Combine x and -x to get 0.

$$-2-\left(-\left(-x\right)\right)=0$$

Add 2 to both sides. Anything plus zero gives itself.

$$-\left(-\left(-x\right)\right)=2$$

Divide both sides by -1.

$$-\left(-1\right)x=-2$$

Divide both sides by -1.

$$-x=\frac{-2}{-1}$$

Fraction \frac{-2}{-1} can be simplified to 2 by removing the negative sign from both the numerator and the denominator.

$$-x=2$$

Multiply both sides by -1.

$$x=-2$$