Solution - Absolute value equations

$$\left(-7x-3\right)-7x=\left(7x+3\right)-7x$$

Group like terms:

$$\left(-7x-7x\right)-3=\left(7x+3\right)-7x$$

Simplify the arithmetic:

$$-14x-3=\left(7x+3\right)-7x$$

Group like terms:

$$-14x-3=\left(7x-7x\right)+3$$

Simplify the arithmetic:

$$-14x-3=3$$

Add $$$$ to both sides:

$$\left(-14x-3\right)+3=3+3$$

Simplify the arithmetic:

$$-14x=3+3$$

Simplify the arithmetic:

$$-14x=6$$

Divide both sides by :

$$\frac{\left(-14x\right)}{-14}=\frac{6}{-14}$$

Cancel out the negatives:

$$\frac{14x}{14}=\frac{6}{-14}$$

Simplify the fraction:

$$x=\frac{6}{-14}$$

Move the negative sign from the denominator to the numerator:

$$x=\frac{-6}{14}$$

Find the greatest common factor of the numerator and denominator:

$$x=\frac{\left(-3·2\right)}{\left(7·2\right)}$$

Factor out and cancel the greatest common factor:

$$x=\frac{-3}{7}$$

$$\left(-7x-3\right)=-7x-3$$

Add $$$$ to both sides:

$$\left(-7x-3\right)+7x=\left(-7x-3\right)+7x$$

Group like terms:

$$\left(-7x+7x\right)-3=\left(-7x-3\right)+7x$$

Simplify the arithmetic:

$$-3=\left(-7x-3\right)+7x$$

Group like terms:

$$-3=\left(-7x+7x\right)-3$$

Simplify the arithmetic:

$$-3=-3$$