Question

what is the inverse of the following statement? if $3x = 12$, then $x = 4$. if $3x \
eq 12$, then $x \
eq 4$. if $x = 4$, then $3x = 12$.

Explanation:

Step1: Recall the definition of inverse of a conditional statement

A conditional statement is of the form "If \( p \), then \( q \)". The inverse of this statement is "If not \( p \), then not \( q \)".

Step2: Identify \( p \) and \( q \) in the given statement

In the statement "If \( 3x = 12 \), then \( x = 4 \)", \( p \) is \( 3x = 12 \) and \( q \) is \( x = 4 \).

Step3: Find the negation of \( p \) and \( q \)

The negation of \( p \) ( \( 3x = 12 \)) is \( 3x
eq 12 \), and the negation of \( q \) ( \( x = 4 \)) is \( x
eq 4 \).

Step4: Form the inverse statement

Using the definition of inverse, the inverse of "If \( 3x = 12 \), then \( x = 4 \)" is "If \( 3x
eq 12 \), then \( x
eq 4 \)".

Answer:

If \( 3x
eq 12 \), then \( x
eq 4 \)