Two-column Algebraic Proofs Practice Worksheet for solving equations with step-by-step reasoning.

1)
b. -4x + 10 + 5x = -5x + 18 + 5x Addition Prop. of Equality
c. x + 10 = 18 Simplify
d. x = 8 Substitution Prop.

2)
b. 4x - 12x = 12x + 32 - 12x Subtraction Prop. of Equality
c. -8x = 32 Simplify
d. x = -4 Division Prop. of Equality

3)
b. 2 * (3x + 5)/2 = 2 * 7 Multiplication Prop. of Equality
c. 3x + 5 = 14 Simplify
d. 3x = 9 Subtraction Prop. of Equality
e. x = 3 Division Prop. of Equality

4)
b. 5x + 10 = -3x - 6 Distributive Prop.
c. 5x + 10 + 3x = -3x - 6 + 3x Addition Prop. of Equality
d. 8x + 10 = -6 Simplify
e. 8x = -16 Subtraction Prop. of Equality
f. x = -2 Division Prop. of Equality

5)
b. 4 + 6x + 10 = 11 - x Distributive Prop.
c. 6x + 14 = 11 - x Simplify
d. 6x + 14 + x = 11 - x + x Addition Prop. of Equality
e. 7x + 14 = 11 Simplify
f. 7x = -3 Subtraction Prop. of Equality
g. x = -3/7 Division Prop. of Equality

6)
b. 3 + 4x - 8 = 27 Distributive Prop.
c. 4x - 5 = 27 Simplify
d. 4x = 32 Addition Prop. of Equality
e. x = 8 Division Prop. of Equality