To find how many solutions the equation \( 13b + 18 = 17b - 6 - 16b \) has, we can start by simplifying the equation:
-
Combine like terms on the right side: \[ 17b - 16b = b \] Thus, the equation becomes: \[ 13b + 18 = b - 6 \]
-
Next, we isolate \( b \) by subtracting \( b \) from both sides: \[ 13b - b + 18 = -6 \] Simplifying the left side gives: \[ 12b + 18 = -6 \]
-
Now, subtract 18 from both sides: \[ 12b = -6 - 18 \] Thus, \[ 12b = -24 \]
-
Finally, divide both sides by 12: \[ b = \frac{-24}{12} = -2 \]
Since we obtained a single value for \( b \), the equation has one solution: \( b = -2 \).