Solution - Absolute value equations

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

Add $$$$ to both sides:

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

Group like terms:

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

Simplify the arithmetic:

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

Group like terms:

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

Simplify the arithmetic:

$$2x+3=-3$$

Subtract $$$$ from both sides:

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

Simplify the arithmetic:

$$2x=-3-3$$

Simplify the arithmetic:

$$2x=-6$$

Divide both sides by :

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

Simplify the fraction:

$$x=\frac{-6}{2}$$

Find the greatest common factor of the numerator and denominator:

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

Factor out and cancel the greatest common factor:

$$x=-3$$

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

Subtract $$$$ from both sides:

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

Group like terms:

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

Simplify the arithmetic:

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

Group like terms:

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

Simplify the arithmetic:

$$3=3$$