To determine the number of solutions to the equation [tex]\( 8x + 47 = 8(x + 5) \)[/tex], let's go through a step-by-step analysis.
1. Start with the given equation:
[tex]\[
8x + 47 = 8(x + 5)
\][/tex]
2. Distribute the 8 on the right-hand side:
[tex]\[
8x + 47 = 8x + 40
\][/tex]
3. Next, subtract [tex]\( 8x \)[/tex] from both sides of the equation:
[tex]\[
8x + 47 - 8x = 8x + 40 - 8x
\][/tex]
Simplifying this, we get:
[tex]\[
47 = 40
\][/tex]
4. We see that [tex]\( 47 = 40 \)[/tex] is a contradiction since 47 is not equal to 40.
Therefore, the equation [tex]\( 8x + 47 = 8(x + 5) \)[/tex] has no solutions.
So, the correct answer is:
B. No solution
