To find:The given statement is true or false.General strategy to solve

Tolnaio

Tolnaio

Answered question

2021-10-17

To find:
The given statement is true or false.
General strategy to solve the inequalities that involve absolute value:
Absolute value inequalities deal with the inequalities (<,>,,and) on the expressions with absolute sign.
General properties for solving inequalities that involve absolute value are
1) |x|>k is equivalent to x<k or x>k, where k is positive number.
2) |x|<k is equivalent to xk and x<k, where k is a positive number and we can write a conjunction such as xk and x<k in the compact form k<x<k.
If k is a non positive number, we can determine the solution sets by inspection.

Answer & Explanation

pattererX

pattererX

Skilled2021-10-18Added 95 answers

Calculation:
To find the solution set for |x2|6 is all real numbers:
The given equation is of the form of |x|>k. However, the standard method for solving inequalities that involve absolute value cannot be applied to |x2|6 because k is negative.
We will solve the given equation |x2|6 by inspection.
|x2|6 is satisfied by all real numbers because the absolute value of (x2), regardless of what number is substituted for x, will always be greater than or equal to -6.
The solution set is the set of all real numbers, which we can express in interval notation as (,).
Conclusion:
Absolute values are always greater or equal to 0. So the given statement is true.

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