Answer:
Converse: B. If x = 5, then 4x + 7 = 27
Inverse: If 4x + 7 ≠ 27, then x ≠ 5
Contrapositive: If x ≠ 5, then 4x + 7 ≠ 27
Explanations:
To find the converse of a statement, the hypothesis should become the conclusion, and vice-versa.
That is, for a statement like:
If P, then Q, P → Q
The converse will be:
If Q, then P, Q→ P
Following the rule above, the converse of the statement:
"If 4x + 7 = 27, then x = 5" will be
" If x = 5, then 4x + 7 = 27"
For a statement "
If P, then Q, P → Q
The inverse will be:
If ∼P, then ∼Q, ∼P → ∼Q
Following the rule above, the inverse of the statement:
"If 4x + 7 = 27, then x = 5" will be
"If 4x + 7 ≠ 27, then x ≠ 5 "
For a statement, " If P, then Q", the contrapositive will be "If not Q, then not P"
If P, then Q, P → Q
The contrapositive will be:
If ∼Q, then ∼P, ∼Q → ∼P
Following the rule above, the converse of the statement:
"If 4x + 7 = 27, then x = 5" will be
" If x ≠ 5, then 4x + 7 ≠ 27"