To determine the formula that represents "8 less than twice a number," let's break down the phrase step-by-step:
1. "Twice a number" means you multiply the number by 2. If we let the number be represented by [tex]\( w \)[/tex], then twice the number is [tex]\( 2w \)[/tex].
2. "8 less than" this result means we subtract 8 from [tex]\( 2w \)[/tex]. Mathematically, this can be expressed as [tex]\( 2w - 8 \)[/tex].
Thus, the correct formula is
[tex]\[ q = 2w - 8 \][/tex]
Comparing this with the given choices:
- [tex]\( q = 8w - 2 \)[/tex] is not correct because instead of subtracting 8, it is subtracting 2 and incorrectly multiplying 8 by [tex]\( w \)[/tex].
- [tex]\( q = 2w - 8 \)[/tex] is correct as it matches our derived formula.
- [tex]\( q = 10w \)[/tex] is not correct because it does not properly subtract 8 and it incorrectly multiplies 10 by [tex]\( w \)[/tex].
- [tex]\( q = 6w \)[/tex] is not correct as it does not include the subtraction of 8 and incorrectly multiplies 6 by [tex]\( w \)[/tex].
So, the correct formula is
[tex]\[ q = 2w - 8 \][/tex]
