To determine the number of solutions to the given equation
[tex]\[
8x + 47 = 8(x + 5),
\][/tex]
we start by simplifying and analyzing the equation step-by-step.
1. Expand and simplify the equation:
Begin by expanding the right-hand side of the equation:
[tex]\[
8x + 47 = 8x + 40.
\][/tex]
2. Isolate the variable term:
Subtract [tex]\(8x\)[/tex] from both sides of the equation to isolate the constant terms:
[tex]\[
8x + 47 - 8x = 8x + 40 - 8x.
\][/tex]
Simplifying this, we get:
[tex]\[
47 = 40.
\][/tex]
3. Analyze the resulting equation:
The simplified equation is [tex]\(47 = 40\)[/tex], which is a false statement.
Since the resulting statement [tex]\(47 = 40\)[/tex] is false, it implies that there are no values of [tex]\(x\)[/tex] that can satisfy the original equation. Therefore, the original equation has no solutions.
Thus, the number of solutions to the equation is
[tex]\[
\boxed{0}.
\][/tex]
