31=4v+7(v+6)

Solution for 31=4v+7(v+6) equation:

Simplifying
31 = 4v + 7(v + 6)

Reorder the terms:
31 = 4v + 7(6 + v)
31 = 4v + (6 * 7 + v * 7)
31 = 4v + (42 + 7v)

Reorder the terms:
31 = 42 + 4v + 7v

Combine like terms: 4v + 7v = 11v
31 = 42 + 11v

Solving
31 = 42 + 11v

Solving for variable 'v'.

Move all terms containing v to the left, all other terms to the right.

Add '-11v' to each side of the equation.
31 + -11v = 42 + 11v + -11v

Combine like terms: 11v + -11v = 0
31 + -11v = 42 + 0
31 + -11v = 42

Add '-31' to each side of the equation.
31 + -31 + -11v = 42 + -31

Combine like terms: 31 + -31 = 0
0 + -11v = 42 + -31
-11v = 42 + -31

Combine like terms: 42 + -31 = 11
-11v = 11

Divide each side by '-11'.
v = -1

Simplifying
v = -1