We can add 2x-6 to both sides of the equation.

(12x +6) + (2x -6) = (31 -2x) + (2x -6)

x(12 + 2) +6 -6 = 31 -6 -2x +2x

14x = 25

Multiply both sides of the equation by 1/14.

14x(1/14) = 25(1/14)

x = 25/14

In linear equations the variables are multiplied by a constant and added together. To "undo" those operations, we must use addition to add the additive inverse of terms we want to cancel, and we must use multiplication to multiply by the multiplicative inverse to eliminate coefficients we don't want.

Check

12(25/14) + 6 = 31 - 2(25/14)

300/14 + 84/14 = 434/14 - 50/14

384/14 = 384/14 (yes)

(12x +6) + (2x -6) = (31 -2x) + (2x -6)

x(12 + 2) +6 -6 = 31 -6 -2x +2x

14x = 25

Multiply both sides of the equation by 1/14.

14x(1/14) = 25(1/14)

x = 25/14

In linear equations the variables are multiplied by a constant and added together. To "undo" those operations, we must use addition to add the additive inverse of terms we want to cancel, and we must use multiplication to multiply by the multiplicative inverse to eliminate coefficients we don't want.

Check

12(25/14) + 6 = 31 - 2(25/14)

300/14 + 84/14 = 434/14 - 50/14

384/14 = 384/14 (yes)