To find the inverse of a given conditional statement, we need to negate both the hypothesis and the conclusion of the original statement.
The original statement is:
"If [tex]\( 2x + 1 = 5 \)[/tex], then [tex]\( x = 2 \)[/tex]."
Let's break it down step-by-step:
1. Identify the hypothesis and conclusion:
- Hypothesis: [tex]\( 2x + 1 = 5 \)[/tex]
- Conclusion: [tex]\( x = 2 \)[/tex]
2. Negate both the hypothesis and the conclusion:
- Negating the hypothesis [tex]\( 2x + 1 = 5 \)[/tex] becomes [tex]\( 2x + 1 \neq 5 \)[/tex].
- Negating the conclusion [tex]\( x = 2 \)[/tex] becomes [tex]\( x \neq 2 \)[/tex].
3. Form the inverse statement:
- Combining the negated hypothesis and negated conclusion: "If [tex]\( 2x + 1 \neq 5 \)[/tex], then [tex]\( x \neq 2 \)[/tex]."
Thus, the inverse of the conditional statement "If [tex]\( 2x + 1 = 5 \)[/tex], then [tex]\( x = 2 \)[/tex]" is:
"If [tex]\( 2x + 1 \neq 5 \)[/tex], then [tex]\( x \neq 2 \)[/tex]."
So the correct answer is:
"If [tex]\( 2x + 1 \neq 5 \)[/tex], then [tex]\( x \neq 2 \)[/tex]."
