Let's simplify the equation step by step:
The original equation is: \[ 13b + 18 = 17b - 6 - 16b \]
First, simplify the right side of the equation: \[ 17b - 16b = b \] So the equation now is: \[ 13b + 18 = b - 6 \]
Next, we can isolate \(b\) by moving all terms involving \(b\) to one side and constant terms to the other side. Subtract \(b\) from both sides: \[ 13b - b + 18 = -6 \] This simplifies to: \[ 12b + 18 = -6 \]
Now, subtract 18 from both sides: \[ 12b = -6 - 18 \] \[ 12b = -24 \]
Now, divide both sides by 12: \[ b = -2 \]
So, the equation \(13b + 18 = 17b - 6 - 16b\) has exactly one solution, \(b = -2\).