To determine the converse of the implication [tex]\( p \rightarrow q \)[/tex], we first need to understand what the converse of an implication means.
Given:
[tex]\[
\begin{array}{ll}
p: & 2x = 16 \\
q: & 3x - 4 = 20
\end{array}
\][/tex]
The original implication statement is [tex]\( p \rightarrow q \)[/tex]:
"If [tex]\( 2x = 16 \)[/tex], then [tex]\( 3x - 4 = 20 \)[/tex]."
The converse of an implication [tex]\( p \rightarrow q \)[/tex] is [tex]\( q \rightarrow p \)[/tex]. This means that we switch the hypothesis and the conclusion of the original implication.
So, for our given statements:
- [tex]\( p \)[/tex]: [tex]\( 2x = 16 \)[/tex]
- [tex]\( q \)[/tex]: [tex]\( 3x - 4 = 20 \)[/tex]
The converse [tex]\( q \rightarrow p \)[/tex] would be:
"If [tex]\( 3x - 4 = 20 \)[/tex], then [tex]\( 2x = 16 \)[/tex]."
Now, let's review the given options to identify the one that correctly represents [tex]\( q \rightarrow p \)[/tex]:
1. If [tex]\( 2x \neq 16 \)[/tex], then [tex]\( 3x - 4 \neq 20 \)[/tex].
2. If [tex]\( 3x - 4 \neq 20 \)[/tex], then [tex]\( 2x \neq 16 \)[/tex].
3. If [tex]\( 2x = 16 \)[/tex], then [tex]\( 3x - 4 = 20 \)[/tex].
4. If [tex]\( 3x - 4 = 20 \)[/tex], then [tex]\( 2x = 16 \)[/tex].
Matching this with our identified converse statement, the correct choice is:
"If [tex]\( 3x - 4 = 20 \)[/tex], then [tex]\( 2x = 16 \)[/tex]."
Therefore, the correct answer is option 4.
