Here's a little more detail on how to analyze the English language
and translate it into the language of algebra:
Eight less than the product of eleven and a number
Eight less than the product of eleven and a number
Replace the words "a number" by "x".
Eight less than the product of eleven and x
Eight less than the product of eleven and x
Replace the word "Eight" by "8" and the word "eleven" by 11:
8 less than the product of 11 and x
8 less than the product of 11 and x
Replace the words "the product of 11 and x" by "11x"
8 less than 11x
To make something 8 less than it is, you subtract 8 from it.
We want to make llx to be 8 less than it is, so we subtract 8
from it:
11x - 8
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Ten times the difference between a number and Fifty.
Ten times the difference between a number and Fifty.
Replace the words "a number" by x, the word "ten" by 10, and "fifty" by "50"
10 times the difference between x and 50.
10 times the difference between x and 50.
Replace the words "the difference between x and 50" by "(x-50)"
10 times (x-50)
Replace that by
10(x-50)
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The product of 9 and the total of z and 4
The product of 9 and the total of z and 4
To find a total of two things you put a plus between them, so
replace the words "the total of z and 4" by "(z+4)"
The product of 9 and (z+4)
Replace that by
9(z+4)
Edwin
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