Solution - Absolute value equations

$$-2n-2·7=\left(4n+8\right)$$

Simplify the arithmetic:

$$-2n-14=\left(4n+8\right)$$

Subtract $$$$ from both sides:

$$\left(-2n-14\right)-4n=\left(4n+8\right)-4n$$

Group like terms:

$$\left(-2n-4n\right)-14=\left(4n+8\right)-4n$$

Simplify the arithmetic:

$$-6n-14=\left(4n+8\right)-4n$$

Group like terms:

$$-6n-14=\left(4n-4n\right)+8$$

Simplify the arithmetic:

$$-6n-14=8$$

Add $$$$ to both sides:

$$\left(-6n-14\right)+14=8+14$$

Simplify the arithmetic:

$$-6n=8+14$$

Simplify the arithmetic:

$$-6n=22$$

Divide both sides by :

$$\frac{\left(-6n\right)}{-6}=\frac{22}{-6}$$

Cancel out the negatives:

$$\frac{6n}{6}=\frac{22}{-6}$$

Simplify the fraction:

$$n=\frac{22}{-6}$$

Move the negative sign from the denominator to the numerator:

$$n=\frac{-22}{6}$$

Find the greatest common factor of the numerator and denominator:

$$n=\frac{\left(-11·2\right)}{\left(3·2\right)}$$

Factor out and cancel the greatest common factor:

$$n=\frac{-11}{3}$$

$$-2n-2·7=-\left(4n+8\right)$$

Simplify the arithmetic:

$$-2n-14=-\left(4n+8\right)$$

Expand the parentheses:

$$-2n-14=-4n-8$$

Add $$$$ to both sides:

$$\left(-2n-14\right)+4n=\left(-4n-8\right)+4n$$

Group like terms:

$$\left(-2n+4n\right)-14=\left(-4n-8\right)+4n$$

Simplify the arithmetic:

$$2n-14=\left(-4n-8\right)+4n$$

Group like terms:

$$2n-14=\left(-4n+4n\right)-8$$

Simplify the arithmetic:

$$2n-14=-8$$

Add $$$$ to both sides:

$$\left(2n-14\right)+14=-8+14$$

Simplify the arithmetic:

$$2n=-8+14$$

Simplify the arithmetic:

$$2n=6$$

Divide both sides by :

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

Simplify the fraction:

$$n=\frac{6}{2}$$

Find the greatest common factor of the numerator and denominator:

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

Factor out and cancel the greatest common factor:

$$n=3$$