Final answer:
The inverse of the conditional statement 'if p then q', where p is '7x+1=8' and q is '3x+4=7', is 'if 7x+1 is not equal to 8, then 3x+4 is not equal to 7'.
Step-by-step explanation:
You've been given two propositions, p and q, with p being '7x+1=8' and q being '3x+4=7'. The conditional statement p → q can be read as 'if p then q'. To write the inverse of this conditional statement, you negate both the hypothesis and the conclusion. So, the inverse would be 'if not p then not q'.
In symbolic form, the inverse of p → q is ¬p → ¬q. When we translate the original statements into their negations, we get ¬p: 7x+1 ≠ 8 (7x+1 is not equal to 8) and ¬q: 3x+4 ≠ 7 (3x+4 is not equal to 7). Therefore, the inverse in if-then form is 'if 7x+1 is not equal to 8, then 3x+4 is not equal to 7'.