Solution - Absolute value equations

$$\left(2x+1\right)=-7x-5$$

Add $$$$ to both sides:

$$\left(2x+1\right)+7x=\left(-7x-5\right)+7x$$

Group like terms:

$$\left(2x+7x\right)+1=\left(-7x-5\right)+7x$$

Simplify the arithmetic:

$$9x+1=\left(-7x-5\right)+7x$$

Group like terms:

$$9x+1=\left(-7x+7x\right)-5$$

Simplify the arithmetic:

$$9x+1=-5$$

Subtract $$$$ from both sides:

$$\left(9x+1\right)-1=-5-1$$

Simplify the arithmetic:

$$9x=-5-1$$

Simplify the arithmetic:

$$9x=-6$$

Divide both sides by :

$$\frac{\left(9x\right)}{9}=\frac{-6}{9}$$

Simplify the fraction:

$$x=\frac{-6}{9}$$

Find the greatest common factor of the numerator and denominator:

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

Factor out and cancel the greatest common factor:

$$x=\frac{-2}{3}$$

$$\left(2x+1\right)=7x+5$$

Subtract $$$$ from both sides:

$$\left(2x+1\right)-7x=\left(7x+5\right)-7x$$

Group like terms:

$$\left(2x-7x\right)+1=\left(7x+5\right)-7x$$

Simplify the arithmetic:

$$-5x+1=\left(7x+5\right)-7x$$

Group like terms:

$$-5x+1=\left(7x-7x\right)+5$$

Simplify the arithmetic:

$$-5x+1=5$$

Subtract $$$$ from both sides:

$$\left(-5x+1\right)-1=5-1$$

Simplify the arithmetic:

$$-5x=5-1$$

Simplify the arithmetic:

$$-5x=4$$

Divide both sides by :

$$\frac{\left(-5x\right)}{-5}=\frac{4}{-5}$$

Cancel out the negatives:

$$\frac{5x}{5}=\frac{4}{-5}$$

Simplify the fraction:

$$x=\frac{4}{-5}$$

Move the negative sign from the denominator to the numerator:

$$x=\frac{-4}{5}$$