Fergznaniidn
Answered

IDNLearn.com provides a collaborative environment for finding and sharing answers. Get timely and accurate answers to your questions from our dedicated community of experts who are here to help you.

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 :

GinnyAnsweridn
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]."
We are happy to have you as part of our community. Keep asking, answering, and sharing your insights. Together, we can create a valuable knowledge resource. Trust IDNLearn.com for all your queries. We appreciate your visit and hope to assist you again soon.