Answer
The solutions are $b=3$ and $b=5$.
Work Step by Step
The given equation is
$\Rightarrow |2b-9|=|b-6|$
Write the two related linear equations.
$2b-9=b-6$ ...... (1)
$2b-9=-(b-6)$ ...... (2)
Solve equation (1).
$\Rightarrow 2b-9=b-6$
Add $9-b$ to each side.
$\Rightarrow 2b-9+9-b=b-6+9-b$
Simplify.
$\Rightarrow b=3$
Check : $b=3$
$\Rightarrow |2b-9|=|b-6|$
$\Rightarrow |2(3)-9|=|3-6|$
$\Rightarrow |6-9|=|-3|$
$\Rightarrow |-3|=|-3|$
True.
Solve equation (2).
$\Rightarrow 2b-9=-(b-6)$
Simplify.
$\Rightarrow 2b-9=-b+6$
Add $9+b$ to each side.
$\Rightarrow 2b-9+9+b=-b+6+9+b$
Simplify.
$\Rightarrow 3b=15$
Divide each side by $3$.
$\Rightarrow \frac{3b}{3}=\frac{15}{3}$
Simplify.
$\Rightarrow b=5$
Check : $b=5$
$\Rightarrow |2b-9|=|b-6|$
$\Rightarrow |2(5)-9|=|5-6|$
$\Rightarrow |10-9|=|-1|$
$\Rightarrow |1|=|-1|$
$\Rightarrow 1=1$
True.
Hence, the solutions are $b=3$ and $b=5$.
