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 = 10
B no solution
C single solution
D infinitely many solutions

Answer 1

To determine the nature of the solution for the equation \( 3x + 7(x + 1) = 2(6x + 5) - 2x \), let's simplify both sides.

Start by expanding and simplifying:

### Left Side:

\[
3x + 7(x + 1) = 3x + 7x + 7 = 10x + 7
\]

### Right Side:

\[
2(6x + 5) - 2x = 12x + 10 - 2x = 10x + 10
\]

Now the equation looks like this:

\[
10x + 7 = 10x + 10
\]

Next, we will isolate \( x \):

Subtract \( 10x \) from both sides:

\[
7 = 10
\]

This statement is false, meaning that there are no values of \( x \) that satisfy the equation. Therefore, the answer is:

**B. no solution.**