How do I write a two column proof with the conjecture -3/2=2+7/2x

Answer 1

The equation suggests x=-1, so

we start with -3/2 and work backwards,

introducing x=-1 at the end

Statement Reason

-3/2 = -3/2 Reflexive

4/2 - 7/4 = -3/2 Subtraction of fractions

4/2 = 2 division of fractions

-3/2 = 4/2 - 7/2 substitution

-3/2 = 2 - 7/2 substitution

-3/2 = 2 + -7/2 definition of subtraction

-3/2 = 2 + (-1)(7/2) property of -1

-3/2 = 2 + (7/2)(-1) commutative property of multiplciation

Let x = -1 closure property of reals

-3/2 = 2 + (7/2)x substitution

end of proof