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5 votes
If x<0 then

Select one:

a. x|x|<0
b. x|x|2>0
c. x|x|>0
d. x+|x|>0
e. x−|x|>0

1 Answer

4 votes

Answer:

A

Explanation:

if x < 0, then by the definition of the absolute value function, |x| > 0. this is because the absolute value function turns whatever is inside the function, whether positive or negative, into positive.

also, the product of a negative number and a positive number is negative.

let's do them step by step.

a) x|x|<0 is the product of a negative value (x) and a positive value (|x|). as mentioned earlier the product of the following is negative. thus, this is true.

b) x|x|²>0 is again, the product of a negative value (x) and a positive value (|x|², since the square of any value is positive). so the product is negative. thus, this statement is false.

c) x|x|>0 is false, as established from (a).

d) note that here x is the negative of |x| so essentially it is the additive inverse of |x|. by definition the sum of a number and it's additive inverse is equal to 0. (additive inverse of n is -n).

so, we have x+|x|=0, however the statement is false since it is inequality, not equality. it will never take values greater than 0.

e) lastly, -|x| can be expressed simply as x, so we have the sum 2x>0, which is false as x<0.

therefore, our only solution is (a)

User Berkelem
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