Certainly! Let's follow a clear, step-by-step process to represent the variable [tex]\( l \)[/tex] in terms of [tex]\( V \)[/tex] and [tex]\( b \)[/tex] using the given equation:
The initial given equation is:
[tex]\[ V = 7l + 10b + 20 \][/tex]
### Step 1: Rearrange the Equation
We want to isolate [tex]\( l \)[/tex] on one side of the equation. To do this, we need to get rid of the terms involving [tex]\( b \)[/tex] and the constant on the right-hand side. We start by subtracting [tex]\( 10b \)[/tex] and 20 from both sides of the equation.
[tex]\[ V - 10b - 20 = 7l \][/tex]
### Step 2: Solve for [tex]\( l \)[/tex]
Now that we have isolated the term involving [tex]\( l \)[/tex] on one side of the equation, we want to solve for [tex]\( l \)[/tex]. To isolate [tex]\( l \)[/tex], we divide both sides of the equation by 7.
[tex]\[ l = \frac{V - 10b - 20}{7} \][/tex]
### Conclusion
We have successfully represented [tex]\( l \)[/tex] in terms of [tex]\( V \)[/tex] and [tex]\( b \)[/tex]. The final expression is:
[tex]\[ l = \frac{V - 10b - 20}{7} \][/tex]
