Certainly! Let's solve the equation [tex]\( a(b+c) = a(d-e) \)[/tex] for [tex]\( b \)[/tex].
### Step-by-Step Solution:
Step 1: Examine the given equation
The given equation is:
[tex]\[ a(b + c) = a(d - e) \][/tex]
Step 2: Divide both sides by [tex]\( a \)[/tex]
Since [tex]\( a \neq 0 \)[/tex], we can divide both sides of the equation by [tex]\( a \)[/tex]:
[tex]\[ \frac{a(b + c)}{a} = \frac{a(d - e)}{a} \][/tex]
This simplifies to:
[tex]\[ b + c = d - e \][/tex]
Step 3: Isolate [tex]\( b \)[/tex]
To isolate [tex]\( b \)[/tex], we need to get rid of [tex]\( c \)[/tex] on the left-hand side. We do this by subtracting [tex]\( c \)[/tex] from both sides of the equation:
[tex]\[ b + c - c = (d - e) - c \][/tex]
This simplifies to:
[tex]\[ b = (d - e) - c \][/tex]
So, the solution for [tex]\( b \)[/tex] in terms of [tex]\( c \)[/tex], [tex]\( d \)[/tex], and [tex]\( e \)[/tex] is:
[tex]\[ b = (d - e) - c \][/tex]
Thus, the formula to solve for [tex]\( b \)[/tex] is:
[tex]\[ \boxed{b = (d - e) - c} \][/tex]
