Solution - Absolute value equations

$$\left(x+1\right)=3x+3·3$$

Simplify the arithmetic:

$$\left(x+1\right)=3x+9$$

Subtract $$$$ from both sides:

$$\left(x+1\right)-3x=\left(3x+9\right)-3x$$

Group like terms:

$$\left(x-3x\right)+1=\left(3x+9\right)-3x$$

Simplify the arithmetic:

$$-2x+1=\left(3x+9\right)-3x$$

Group like terms:

$$-2x+1=\left(3x-3x\right)+9$$

Simplify the arithmetic:

$$-2x+1=9$$

Subtract $$$$ from both sides:

$$\left(-2x+1\right)-1=9-1$$

Simplify the arithmetic:

$$-2x=9-1$$

Simplify the arithmetic:

$$-2x=8$$

Divide both sides by :

$$\frac{\left(-2x\right)}{-2}=\frac{8}{-2}$$

Cancel out the negatives:

$$\frac{2x}{2}=\frac{8}{-2}$$

Simplify the fraction:

$$x=\frac{8}{-2}$$

Move the negative sign from the denominator to the numerator:

$$x=\frac{-8}{2}$$

Find the greatest common factor of the numerator and denominator:

$$x=\frac{\left(-4·2\right)}{\left(1·2\right)}$$

Factor out and cancel the greatest common factor:

$$x=-4$$

$$\left(x+1\right)=3·\left(-x-3\right)$$

$$\left(x+1\right)=3·-x+3·-3$$

Group like terms:

$$\left(x+1\right)=\left(3·-1\right)x+3·-3$$

Multiply the coefficients:

$$\left(x+1\right)=-3x+3·-3$$

Simplify the arithmetic:

$$\left(x+1\right)=-3x-9$$

Add $$$$ to both sides:

$$\left(x+1\right)+3x=\left(-3x-9\right)+3x$$

Group like terms:

$$\left(x+3x\right)+1=\left(-3x-9\right)+3x$$

Simplify the arithmetic:

$$4x+1=\left(-3x-9\right)+3x$$

Group like terms:

$$4x+1=\left(-3x+3x\right)-9$$

Simplify the arithmetic:

$$4x+1=-9$$

Subtract $$$$ from both sides:

$$\left(4x+1\right)-1=-9-1$$

Simplify the arithmetic:

$$4x=-9-1$$

Simplify the arithmetic:

$$4x=-10$$

Divide both sides by :

$$\frac{\left(4x\right)}{4}=\frac{-10}{4}$$

Simplify the fraction:

$$x=\frac{-10}{4}$$

Find the greatest common factor of the numerator and denominator:

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

Factor out and cancel the greatest common factor:

$$x=\frac{-5}{2}$$