To find an equation equivalent to [tex]\( P = 2(l + w) \)[/tex] and solve for [tex]\( w \)[/tex], we need to isolate [tex]\( w \)[/tex] on one side of the equation. Here are the step-by-step instructions:
1. Start with the original equation:
[tex]\[
P = 2(l + w)
\][/tex]
2. Divide both sides of the equation by 2 to simplify:
[tex]\[
\frac{P}{2} = l + w
\][/tex]
3. Subtract [tex]\( l \)[/tex] from both sides to isolate [tex]\( w \)[/tex]:
[tex]\[
\frac{P}{2} - l = w
\][/tex]
4. This is equivalent to:
[tex]\[
w = \frac{P}{2} - l
\][/tex]
5. To match this with one of the given options, we can rewrite the equation:
[tex]\[
w = \frac{P - 2l}{2}
\][/tex]
Observe that:
- Option [tex]\( w = P - 21 \)[/tex] is not correct because it does not involve [tex]\( l \)[/tex] and the arithmetic is not the same.
- Option [tex]\( w = P - 1 \)[/tex] is also incorrect for the same reasons.
- Option [tex]\( w = \frac{P - 2l}{2} \)[/tex] matches our derived formula.
- Option [tex]\( w = \frac{P + 2!}{2} \)[/tex] is incorrect because it involves factorial and does not correspond mathematically to the derived formula.
Therefore, the equivalent equation to [tex]\( P = 2(l + w) \)[/tex] is:
[tex]\[ w = \frac{P - 2l}{2} \][/tex]
