Solution - Absolute value equations

$$\left(4x+2\right)=-6x-4$$

Add $$$$ to both sides:

$$\left(4x+2\right)+6x=\left(-6x-4\right)+6x$$

Group like terms:

$$\left(4x+6x\right)+2=\left(-6x-4\right)+6x$$

Simplify the arithmetic:

$$10x+2=\left(-6x-4\right)+6x$$

Group like terms:

$$10x+2=\left(-6x+6x\right)-4$$

Simplify the arithmetic:

$$10x+2=-4$$

Subtract $$$$ from both sides:

$$\left(10x+2\right)-2=-4-2$$

Simplify the arithmetic:

$$10x=-4-2$$

Simplify the arithmetic:

$$10x=-6$$

Divide both sides by :

$$\frac{\left(10x\right)}{10}=\frac{-6}{10}$$

Simplify the fraction:

$$x=\frac{-6}{10}$$

Find the greatest common factor of the numerator and denominator:

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

Factor out and cancel the greatest common factor:

$$x=\frac{-3}{5}$$

$$\left(4x+2\right)=6x+4$$

Subtract $$$$ from both sides:

$$\left(4x+2\right)-6x=\left(6x+4\right)-6x$$

Group like terms:

$$\left(4x-6x\right)+2=\left(6x+4\right)-6x$$

Simplify the arithmetic:

$$-2x+2=\left(6x+4\right)-6x$$

Group like terms:

$$-2x+2=\left(6x-6x\right)+4$$

Simplify the arithmetic:

$$-2x+2=4$$

Subtract $$$$ from both sides:

$$\left(-2x+2\right)-2=4-2$$

Simplify the arithmetic:

$$-2x=4-2$$

Simplify the arithmetic:

$$-2x=2$$

Divide both sides by :

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

Cancel out the negatives:

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

Simplify the fraction:

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

Move the negative sign from the denominator to the numerator:

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

Simplify the fraction:

$$x=-1$$