Question
does this equation have infinitely many solutions x+6 = 5x+30
Answers
GPT-4o mini
To determine if the equation \( x + 6 = 5x + 30 \) has infinitely many solutions, we can simplify it.
1. Start by rearranging the equation to isolate \( x \):
\[
x + 6 = 5x + 30
\]
2. Subtract \( x \) from both sides:
\[
6 = 4x + 30
\]
3. Next, subtract 30 from both sides:
\[
6 - 30 = 4x
\]
\[
-24 = 4x
\]
4. Now, divide both sides by 4:
\[
x = -6
\]
Since we found a specific solution \( x = -6 \) and not a statement that is true for all \( x \) (like \( 0 = 0 \)), the equation has only one unique solution.
Therefore, the equation \( x + 6 = 5x + 30 \) does **not** have infinitely many solutions; it has exactly one solution, which is \( x = -6 \).
1. Start by rearranging the equation to isolate \( x \):
\[
x + 6 = 5x + 30
\]
2. Subtract \( x \) from both sides:
\[
6 = 4x + 30
\]
3. Next, subtract 30 from both sides:
\[
6 - 30 = 4x
\]
\[
-24 = 4x
\]
4. Now, divide both sides by 4:
\[
x = -6
\]
Since we found a specific solution \( x = -6 \) and not a statement that is true for all \( x \) (like \( 0 = 0 \)), the equation has only one unique solution.
Therefore, the equation \( x + 6 = 5x + 30 \) does **not** have infinitely many solutions; it has exactly one solution, which is \( x = -6 \).