To explain: whether an absolute value inequality uses a compound inequality with and or a compound inequality with or and to solve absolute value inequalities.
Explanation of Solution
Union represents the logical operator. For example:
Consider the absolute value inequality,
Now, solve the absolute value inequality as shown,
Hence, the solution of the inequality is
No numbers can be there which are at the same time lesser than
So, the statement cannot be connected by the word ‘and’ instead of ‘or’.
So, Compound inequality with ‘or’ is the union of the solution sets of the two inequalities.
Intersection represents the logical operator ‘and’. For example:
Consider the absolute value inequality,
Now, solve the absolute value inequality as shown,
Hence, the solution of the inequality is
No numbers can be there which are at the same time greater than
So, the statement is connected by the word ‘and’ instead of ‘or’.
So, Compound inequality with ‘and’ is the intersection of the solution sets of the two inequalities.
Chapter 6 Solutions
Algebra 1
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