Let's solve the given equation step-by-step to determine the number of solutions.
The equation to solve is:
[tex]\[ 6x + 35 + 9x = 15(x + 4) - 25 \][/tex]
First, combine like terms on the left-hand side:
[tex]\[ 6x + 9x + 35 = 15(x + 4) - 25 \][/tex]
[tex]\[ 15x + 35 = 15(x + 4) - 25 \][/tex]
Next, distribute the 15 on the right-hand side:
[tex]\[ 15x + 35 = 15x + 60 - 25 \][/tex]
[tex]\[ 15x + 35 = 15x + 35 \][/tex]
At this point, we notice that both sides of the equation are identical:
[tex]\[ 15x + 35 = 15x + 35 \][/tex]
This means the equation is true for all values of [tex]\( x \)[/tex], which indicates that there are infinitely many solutions.
Thus, the number of solutions to the equation is:
C. Infinitely many
