The product of 3 less than twice x and 2 more than the quantity 3 times x.
The product of 3 less than twice x and 2 more than the quantity 3 times x
Change the red words to 2x and the green words to 3x. Now you have:
The product of 3 less than 2x and 2 more than 3x.
The product of 3 less than 2x and 2 more than 3x
The red words tell you to start with 2x and then make it 3 less by
subtracting 3 from it, so you put down 2x and then make it less by
putting -3 right after it. So replace the red words by (2x-3). We
put it in parentheses because it contains more than one term.
So now you have:
The product of (2x-3) and 2 more than 3x
The product of (2x-3) and 2 more than 3x
Similarly, the red words tell you to start with 3x and then make it 2 more by
adding 2 to it, so you put down 3x and then make it more by putting +2
right after it. So replace the red words by (3x+2). As before, we put it in
parentheses because it contains more than one term. So now you have:
The product of (2x-3) and (3x+2).
Now "the product of" means to multiply, so we end up the translation from
English to algebra as this multiplication:
(2x-3)(3x+2)
Now we use FOIL:
6x2+4x-9x-6
Combining terms:
6x2-5x-6, choice D
Edwin
