What is absolute value and linear inequality?
Understand the Problem
The question is asking for explanations of the concepts of absolute value and linear inequality. Absolute value refers to the distance of a number from zero on the number line, regardless of direction. A linear inequality is an inequality that involves a linear expression and can be represented on a number line or a coordinate graph.
Answer
Absolute value is the distance from zero; linear inequalities compare expressions using inequality symbols.
Absolute value is the distance of a number from zero on a number line, always a positive value. Linear inequalities involve algebraic expressions that use inequality symbols to compare expressions, like <, >, ≤, or ≥. Absolute value inequalities include absolute values within these comparisons.
Answer for screen readers
Absolute value is the distance of a number from zero on a number line, always a positive value. Linear inequalities involve algebraic expressions that use inequality symbols to compare expressions, like <, >, ≤, or ≥. Absolute value inequalities include absolute values within these comparisons.
More Information
Absolute value is always positive or zero as it represents distance, which cannot be negative. Linear inequalities are often solved by finding the values that make the inequality true and can be represented on a number line.
Tips
A common mistake is misinterpreting the absolute value symbol as a normal parenthesis or misunderstanding that the result of an absolute value cannot be negative.
Sources
- Intro to absolute value inequalities (video) - Khan Academy - khanacademy.org
- 2.6: Solving Absolute Value Equations and Inequalities - math.libretexts.org
- 2.7 Linear Inequalities and Absolute Value Inequalities - OpenStax - openstax.org
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