Question
In the equation, which is true about the value of x?
3x + 7(x + 1) = 2(6x + 5) − 2x
3x + 7(x + 1) = 2(6x + 5) − 2x
Answers
GPT-4o mini
To solve the equation \( 3x + 7(x + 1) = 2(6x + 5) - 2x \), we will first simplify both sides.
Starting with the left side:
\[
3x + 7(x + 1) = 3x + 7x + 7 = 10x + 7
\]
Now, simplifying the right side:
\[
2(6x + 5) - 2x = 12x + 10 - 2x = 10x + 10
\]
Now we have:
\[
10x + 7 = 10x + 10
\]
Next, we will subtract \( 10x \) from both sides:
\[
7 = 10
\]
This is a contradiction, meaning that the left side will never equal the right side for any real value of \( x \).
Thus, the conclusion is that there is no solution for \( x \) in the equation \( 3x + 7(x + 1) = 2(6x + 5) - 2x \).
Starting with the left side:
\[
3x + 7(x + 1) = 3x + 7x + 7 = 10x + 7
\]
Now, simplifying the right side:
\[
2(6x + 5) - 2x = 12x + 10 - 2x = 10x + 10
\]
Now we have:
\[
10x + 7 = 10x + 10
\]
Next, we will subtract \( 10x \) from both sides:
\[
7 = 10
\]
This is a contradiction, meaning that the left side will never equal the right side for any real value of \( x \).
Thus, the conclusion is that there is no solution for \( x \) in the equation \( 3x + 7(x + 1) = 2(6x + 5) - 2x \).