Question
Does this equation have infinite solutions, no solution or one solution?
3x + 18 = 5x + 8
3x + 18 = 5x + 8
Answers
GPT-4o mini
To determine whether the equation \(3x + 18 = 5x + 8\) has infinite solutions, no solution, or one solution, we first simplify the equation.
1. Start by subtracting \(3x\) from both sides:
\[
18 = 5x - 3x + 8
\]
This simplifies to:
\[
18 = 2x + 8
\]
2. Next, subtract 8 from both sides:
\[
18 - 8 = 2x
\]
This simplifies to:
\[
10 = 2x
\]
3. Finally, divide both sides by 2:
\[
x = 5
\]
Since we found a single specific solution (\(x = 5\)), the equation has **one solution**.
1. Start by subtracting \(3x\) from both sides:
\[
18 = 5x - 3x + 8
\]
This simplifies to:
\[
18 = 2x + 8
\]
2. Next, subtract 8 from both sides:
\[
18 - 8 = 2x
\]
This simplifies to:
\[
10 = 2x
\]
3. Finally, divide both sides by 2:
\[
x = 5
\]
Since we found a single specific solution (\(x = 5\)), the equation has **one solution**.