Solution - Absolute value equations

$$\left(v-7\right)-2v=\left(2v-2\right)-2v$$

Group like terms:

$$\left(v-2v\right)-7=\left(2v-2\right)-2v$$

Simplify the arithmetic:

$$-v-7=\left(2v-2\right)-2v$$

Group like terms:

$$-v-7=\left(2v-2v\right)-2$$

Simplify the arithmetic:

$$-v-7=-2$$

Add $$$$ to both sides:

$$\left(-v-7\right)+7=-2+7$$

Simplify the arithmetic:

$$-v=-2+7$$

Simplify the arithmetic:

$$-v=5$$

Multiply both sides by $$$$:

$$-v·-1=5·-1$$

Remove the one(s):

$$v=5·-1$$

Simplify the arithmetic:

$$v=-5$$

$$\left(v-7\right)=-2v+2$$

Add $$$$ to both sides:

$$\left(v-7\right)+2v=\left(-2v+2\right)+2v$$

Group like terms:

$$\left(v+2v\right)-7=\left(-2v+2\right)+2v$$

Simplify the arithmetic:

$$3v-7=\left(-2v+2\right)+2v$$

Group like terms:

$$3v-7=\left(-2v+2v\right)+2$$

Simplify the arithmetic:

$$3v-7=2$$

Add $$$$ to both sides:

$$\left(3v-7\right)+7=2+7$$

Simplify the arithmetic:

$$3v=2+7$$

Simplify the arithmetic:

$$3v=9$$

Divide both sides by :

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

Simplify the fraction:

$$v=\frac{9}{3}$$

Find the greatest common factor of the numerator and denominator:

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

Factor out and cancel the greatest common factor:

$$v=3$$