Solution - Absolute value equations

$$\left(2x+6\right)=5x+15$$

Subtract $$$$ from both sides:

$$\left(2x+6\right)-5x=\left(5x+15\right)-5x$$

Group like terms:

$$\left(2x-5x\right)+6=\left(5x+15\right)-5x$$

Simplify the arithmetic:

$$-3x+6=\left(5x+15\right)-5x$$

Group like terms:

$$-3x+6=\left(5x-5x\right)+15$$

Simplify the arithmetic:

$$-3x+6=15$$

Subtract $$$$ from both sides:

$$\left(-3x+6\right)-6=15-6$$

Simplify the arithmetic:

$$-3x=15-6$$

Simplify the arithmetic:

$$-3x=9$$

Divide both sides by :

$$\frac{\left(-3x\right)}{-3}=\frac{9}{-3}$$

Cancel out the negatives:

$$\frac{3x}{3}=\frac{9}{-3}$$

Simplify the fraction:

$$x=\frac{9}{-3}$$

Move the negative sign from the denominator to the numerator:

$$x=\frac{-9}{3}$$

Find the greatest common factor of the numerator and denominator:

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

Factor out and cancel the greatest common factor:

$$x=-3$$

$$\left(2x+6\right)=-5x-15$$

Add $$$$ to both sides:

$$\left(2x+6\right)+5x=\left(-5x-15\right)+5x$$

Group like terms:

$$\left(2x+5x\right)+6=\left(-5x-15\right)+5x$$

Simplify the arithmetic:

$$7x+6=\left(-5x-15\right)+5x$$

Group like terms:

$$7x+6=\left(-5x+5x\right)-15$$

Simplify the arithmetic:

$$7x+6=-15$$

Subtract $$$$ from both sides:

$$\left(7x+6\right)-6=-15-6$$

Simplify the arithmetic:

$$7x=-15-6$$

Simplify the arithmetic:

$$7x=-21$$

Divide both sides by :

$$\frac{\left(7x\right)}{7}=\frac{-21}{7}$$

Simplify the fraction:

$$x=\frac{-21}{7}$$

Find the greatest common factor of the numerator and denominator:

$$x=\frac{\left(-3·7\right)}{\left(1·7\right)}$$

Factor out and cancel the greatest common factor:

$$x=-3$$