Question

Write a proof for the conjecture using the contrapositive.
If 5x + 7 = -13, then x = -4

Answer 1

Contrapositive: swap the "if" and "then" statements then negate both.

We swap the 5x + 7 = -13 and x = -4 parts first to get

if x = -4 then 5x + 7 = -13

then we negate both statements to get

if x is not equal to -4 then 5x + 7 is not equal to -13

now, you could plug in any x-value not equal to -4 and show that 5x + 7 is not equal to -13, but I think a more robust proof would be to plug in x = -4, show that the result of 5x + 7 *is* -13 and therefore wouldn't be -13 with any other x-value.