Solution - Absolute value equations

$$\left(x-2\right)=2x+2·-5$$

Simplify the arithmetic:

$$\left(x-2\right)=2x-10$$

Subtract $$$$ from both sides:

$$\left(x-2\right)-2x=\left(2x-10\right)-2x$$

Group like terms:

$$\left(x-2x\right)-2=\left(2x-10\right)-2x$$

Simplify the arithmetic:

$$-x-2=\left(2x-10\right)-2x$$

Group like terms:

$$-x-2=\left(2x-2x\right)-10$$

Simplify the arithmetic:

$$-x-2=-10$$

Add $$$$ to both sides:

$$\left(-x-2\right)+2=-10+2$$

Simplify the arithmetic:

$$-x=-10+2$$

Simplify the arithmetic:

$$-x=-8$$

Multiply both sides by $$$$:

$$-x·-1=-8·-1$$

Remove the one(s):

$$x=-8·-1$$

Simplify the arithmetic:

$$x=8$$

$$\left(x-2\right)=2·\left(-x+5\right)$$

$$\left(x-2\right)=2·-x+2·5$$

Group like terms:

$$\left(x-2\right)=\left(2·-1\right)x+2·5$$

Multiply the coefficients:

$$\left(x-2\right)=-2x+2·5$$

Simplify the arithmetic:

$$\left(x-2\right)=-2x+10$$

Add $$$$ to both sides:

$$\left(x-2\right)+2x=\left(-2x+10\right)+2x$$

Group like terms:

$$\left(x+2x\right)-2=\left(-2x+10\right)+2x$$

Simplify the arithmetic:

$$3x-2=\left(-2x+10\right)+2x$$

Group like terms:

$$3x-2=\left(-2x+2x\right)+10$$

Simplify the arithmetic:

$$3x-2=10$$

Add $$$$ to both sides:

$$\left(3x-2\right)+2=10+2$$

Simplify the arithmetic:

$$3x=10+2$$

Simplify the arithmetic:

$$3x=12$$

Divide both sides by :

$$\frac{\left(3x\right)}{3}=\frac{12}{3}$$

Simplify the fraction:

$$x=\frac{12}{3}$$

Find the greatest common factor of the numerator and denominator:

$$x=\frac{\left(4·3\right)}{\left(1·3\right)}$$

Factor out and cancel the greatest common factor:

$$x=4$$