Solution - Absolute value equations

$$\left(x-63\right)+63=\left(-2x\right)+63$$

Simplify the arithmetic:

$$x=\left(-2x\right)+63$$

Add $$$$ to both sides:

$$x+2x=\left(\left(-2x\right)+63\right)+2x$$

Simplify the arithmetic:

$$3x=\left(\left(-2x\right)+63\right)+2x$$

Group like terms:

$$3x=\left(-2x+2x\right)+63$$

Simplify the arithmetic:

$$3x=63$$

Divide both sides by :

$$\frac{\left(3x\right)}{3}=\frac{63}{3}$$

Simplify the fraction:

$$x=\frac{63}{3}$$

Find the greatest common factor of the numerator and denominator:

$$x=\frac{\left(21·3\right)}{\left(1·3\right)}$$

Factor out and cancel the greatest common factor:

$$x=21$$

$$\left(x-63\right)=\left(-1·-2\right)x$$

Multiply the coefficients:

$$\left(x-63\right)=2x$$

Subtract $$$$ from both sides:

$$\left(x-63\right)-2x=\left(2x\right)-2x$$

Group like terms:

$$\left(x-2x\right)-63=\left(2x\right)-2x$$

Simplify the arithmetic:

$$-x-63=\left(2x\right)-2x$$

Simplify the arithmetic:

$$-x-63=0$$

Add $$$$ to both sides:

$$\left(-x-63\right)+63=0+63$$

Simplify the arithmetic:

$$-x=0+63$$

Simplify the arithmetic:

$$-x=63$$

Multiply both sides by $$$$:

$$-x·-1=63·-1$$

Remove the one(s):

$$x=63·-1$$

Simplify the arithmetic:

$$x=-63$$