Let's solve this step-by-step:
We start with the given equation:
[tex]\[ 148 = 2(6w + 6h + hw) \][/tex]
First, distribute the 2 on the right-hand side:
[tex]\[ 148 = 12w + 12h + 2hw \][/tex]
We want to solve for [tex]\( w \)[/tex] in terms of [tex]\( h \)[/tex]. To do this, let's isolate [tex]\( w \)[/tex]:
1. Combine like terms on the right-hand side:
[tex]\[ 148 = 12w + 12h + 2hw \][/tex]
2. Move the [tex]\( 12h \)[/tex] term to the left-hand side:
[tex]\[ 148 - 12h = 12w + 2hw \][/tex]
3. Factor [tex]\( w \)[/tex] out of the terms on the right-hand side:
[tex]\[ 148 - 12h = w(12 + 2h) \][/tex]
4. Divide both sides by [tex]\( (12 + 2h) \)[/tex] to isolate [tex]\( w \)[/tex]:
[tex]\[ w = \frac{148 - 12h}{12 + 2h} \][/tex]
Let's compare this to the given equivalent equations:
- [tex]\( w = \frac{148 - 6h}{12 + h} \)[/tex]
- [tex]\( w = \frac{148 - 12h}{12 + 2h} \)[/tex]
- [tex]\( w = 136 - 14h \)[/tex]
- [tex]\( w = 136 - 10h \)[/tex]
Comparing directly, we see that:
[tex]\[ w = \frac{148 - 12h}{12 + 2h} \][/tex]
is exactly equivalent to our derived equation because both the numerator and denominator match.
Thus, the equivalent equation is:
[tex]\[ w = \frac{148 - 12h}{12 + 2h} \][/tex]
So, the correct equation is:
[tex]\[ w = \frac{148 - 12h}{12 + 2h} \][/tex]
Therefore, the correct answer is the second option:
[tex]\[ w = \frac{148 - 12h}{12 + 2h} \][/tex]
