Absolute Value Inequalities Solve the inequality. Express the answer using interval notation. (1

step 1 Hello, everybody, welcome. Today, we're going to be solving absolute value inequalities, and we'

Absolute Value Inequalities Solve the inequality. Express...

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Key Concepts

Interval Notation

Interval notation is a concise way to represent ranges of real numbers. It uses brackets and parentheses to denote closed and open endpoints, respectively, allowing for a clear depiction of the set of values that satisfy an inequality.

Absolute Value Inequalities

Solving absolute value inequalities often involves rewriting the inequality as a compound inequality. For a form such as |expression| < constant, this method leads to a double inequality that constrains the expression between the negative and positive values of the constant.

Absolute Value

The absolute value of a number or expression represents its distance from zero on the number line, without regard to direction. It is defined as the nonnegative value of the expression inside, making any result always positive or zero.

Rational Expressions and Domain Restrictions

When dealing with expressions that involve absolute values in the denominator, it is crucial to recognize that the denominator cannot be zero. This step ensures that any values making the denominator zero are excluded from the solution set, avoiding undefined expressions in the problem.

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