Ohio Assessments for Educators (OAE) Mathematics Practice Exam

What type of values can make an absolute inequality condition true?

1. Only positive real numbers

2. Any real number

3. Only negative real numbers

4. None of the real numbers

The correct answer is: Any real number

The correct understanding of absolute inequalities lies in recognizing that any real number can satisfy such conditions. Absolute inequalities are expressed in the form |x| < a or |x| > a, where 'x' represents the variable and 'a' is a positive real number. When you have the inequality |x| < a, this implies that 'x' must lie within the range between -a and a, allowing for all real numbers within that interval to satisfy the condition. Thus, any positive, negative, or zero value for 'x' can potentially make the inequality true, as long as it falls within that defined range. Similarly, for |x| > a, it indicates that 'x' must be either less than -a or greater than a, again allowing for any real number that fits these criteria to satisfy the inequality. Since both positive and negative numbers, including zero, can fit into or outside these bounds, it is evident that the statement means all real numbers can be solutions to absolute inequalities. Consequently, the assertion that any real number can make an absolute inequality true is indeed accurate.