The sum of a number and 20 is no more than the sum of the square of the number and 9. which of the following inequalities can be used to determine this unknown number? x + 20 ≤ x2 + 9 x + 20 < x2 + 92 x + 20 < (x + 9)2 x + 20 ≤ (x + 9)2

Per usual with these kinds of questions, the best method is to take the sentence phrase by phrase and translate it accordingly.

Phrase 1: the sum of a number and 20
"The sum" indicates that one side of the inequality is an addition. The two addends, or numbers in the addition problem, are "a number" and 20. Whenever a number is referred without definite value, we can represent it with a variable. With this information, we can say "the sum of a number and 20" translates to "x + 20". I used "x" to represent the number.

Phrase 2: Is no more than 
This indicates that phrase 1, "x + 20" is either equal to or less than whatever is on the other side. Notice how the phrase says "no more" and not "less than". It is only concerned that phrase 1 is not larger than the other side.
Translation: "is no more than" translates to "≤"

Phrase 3: The sum of the square of the number and 9
Again, "sum" refers to an addition problem. This time "the number
, or "x" is raised to the 2nd power or is squared. 
Translation:  + 9

Now that we have our translated inequality, all we have to do is combine all our phrases. Remember to keep the phrases in the order of which they appeared in the sentence.

Final x + 20 ≤  + 9