Question
Solve the equation.
6 x minus 3 equals 6 left parenthesis x plus 4 right parenthesis
Question content area bottom
Part 1
Select the correct choice below and, if necessary, fill in any answer box to complete your answer.
A.
The solution set is StartSet nothing EndSet
.
B.
The solution set is StartSet x vertical line x is a real number EndSet.
C.
The solution set is empty set.
6 x minus 3 equals 6 left parenthesis x plus 4 right parenthesis
Question content area bottom
Part 1
Select the correct choice below and, if necessary, fill in any answer box to complete your answer.
A.
The solution set is StartSet nothing EndSet
.
B.
The solution set is StartSet x vertical line x is a real number EndSet.
C.
The solution set is empty set.
Answers
There are no human answers yet.
Answered by
GPT-4o mini
To solve the equation \( 6x - 3 = 6(x + 4) \), we first expand the right side of the equation:
\[
6x - 3 = 6x + 24
\]
Next, we can subtract \( 6x \) from both sides of the equation:
\[
6x - 6x - 3 = 6x - 6x + 24
\]
\[
-3 = 24
\]
This statement is clearly false. Since we arrived at a contradiction, it means that there are no values of \( x \) that can satisfy the original equation.
Thus, the solution set is empty.
So, the correct choice is:
C. The solution set is the empty set.
\[
6x - 3 = 6x + 24
\]
Next, we can subtract \( 6x \) from both sides of the equation:
\[
6x - 6x - 3 = 6x - 6x + 24
\]
\[
-3 = 24
\]
This statement is clearly false. Since we arrived at a contradiction, it means that there are no values of \( x \) that can satisfy the original equation.
Thus, the solution set is empty.
So, the correct choice is:
C. The solution set is the empty set.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.