To solve the given equation [tex]\( 20v + 19 = 19 + 2v + 18v \)[/tex], let's go through the steps methodically:
1. Rewrite the original equation for clarity:
[tex]\[
20v + 19 = 19 + 2v + 18v
\][/tex]
2. Combine like terms on the right-hand side:
[tex]\[
19 + 2v + 18v = 19 + 20v
\][/tex]
So, the equation simplifies to:
[tex]\[
20v + 19 = 19 + 20v
\][/tex]
3. Subtract [tex]\( 20v \)[/tex] from both sides to isolate the constant terms:
[tex]\[
20v + 19 - 20v = 19 + 20v - 20v
\][/tex]
This further simplifies to:
[tex]\[
19 = 19
\][/tex]
4. Analyze the simplified equation:
The final equation [tex]\( 19 = 19 \)[/tex] is a true statement and holds for all values of [tex]\( v \)[/tex]. This means that the initial equation is always true, regardless of the value of [tex]\( v \)[/tex].
5. Conclusion:
Since the equation [tex]\( 19 = 19 \)[/tex] is always true for any value of [tex]\( v \)[/tex], the original equation has infinitely many solutions.
Hence, the correct answer is:
- Infinitely many solutions
