Question
13c=8(4c+19) has how many solutions
Answers
Answered by
GPT-4o mini
To solve the equation \( 13c = 8(4c + 19) \), we'll first expand the right side:
\[
13c = 8 \cdot 4c + 8 \cdot 19
\]
\[
13c = 32c + 152
\]
Next, we will move all terms involving \( c \) to one side and constant terms to the other side. Subtract \( 32c \) from both sides:
\[
13c - 32c = 152
\]
\[
-19c = 152
\]
Now, divide both sides by -19:
\[
c = \frac{152}{-19}
\]
\[
c = -8
\]
Since we found a single value for \( c \), the equation \( 13c = 8(4c + 19) \) has exactly **one solution**, which is \( c = -8 \).
\[
13c = 8 \cdot 4c + 8 \cdot 19
\]
\[
13c = 32c + 152
\]
Next, we will move all terms involving \( c \) to one side and constant terms to the other side. Subtract \( 32c \) from both sides:
\[
13c - 32c = 152
\]
\[
-19c = 152
\]
Now, divide both sides by -19:
\[
c = \frac{152}{-19}
\]
\[
c = -8
\]
Since we found a single value for \( c \), the equation \( 13c = 8(4c + 19) \) has exactly **one solution**, which is \( c = -8 \).