fergznani
Answered

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Analyze the conditional statement below and complete the instructions that follow:

If [tex]\(2x + 1 = 5\)[/tex], then [tex]\(x = 2\)[/tex].

Identify the inverse of the conditional statement:

A. If [tex]\(x = 2\)[/tex], then [tex]\(2x + 1 = 5\)[/tex].
B. If [tex]\(2x + 1 \neq 5\)[/tex], then [tex]\(x = 2\)[/tex].
C. If [tex]\(2x + 1 \neq 5\)[/tex], then [tex]\(x \neq 2\)[/tex].
D. If [tex]\(x \neq 2\)[/tex], then [tex]\(2x + 1 \neq 5\)[/tex].

Sagot :

GinnyAnswer
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]."
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