Question

Question 7 of 10
How many solutions are there to the equation below?
6x + 35 + 9x = 15(x+ 4) - 25
A. 0
B. Infinitely many
C. 1

Answer 1

To determine how many solutions exist for the equation \( 6x + 35 + 9x = 15(x + 4) - 25 \), let's simplify it step by step.

First, let's simplify the left-hand side of the equation:

\[
6x + 9x + 35 = 15x + 35
\]

Next, simplify the right-hand side. We first distribute \( 15 \):

\[
15(x + 4) = 15x + 60
\]

Now, we can write the entire right-hand side:

\[
15(x + 4) - 25 = 15x + 60 - 25 = 15x + 35
\]

Now putting it all together, we have:

\[
15x + 35 = 15x + 35
\]

This simplifies to:

\[
15x + 35 - 15x - 35 = 0
\]

This results in:

\[
0 = 0
\]

This result means that the equation is an identity, and it holds true for all values of \( x \).

Thus, the number of solutions to the given equation is:

**B. Infinitely many**.