Question

In the equation, which is true about the value of x?

3x + 7(x + 1) = 2(6x + 5) − 2x
Responses
A x = 7, x = 10x
B no solution
C single solution
D infinitely many solutions

Answer 1

To determine the value of \( x \) in the equation \( 3x + 7(x + 1) = 2(6x + 5) - 2x \), let's simplify both sides step by step.

1. Start with the left side:
\[
3x + 7(x + 1) = 3x + 7x + 7 = 10x + 7
\]

2. Now simplify the right side:
\[
2(6x + 5) - 2x = 12x + 10 - 2x = 10x + 10
\]

3. Now we can set the two simplified sides equal to each other:
\[
10x + 7 = 10x + 10
\]

4. Next, subtract \( 10x \) from both sides:
\[
7 = 10
\]

This is a false statement. Therefore, the equation has no solution.

The correct response among the options provided is:
**B no solution**.