Solving Inequalities and Absolute Value Equations

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, greater than or equal to, or less than or equal to the other.

Front

What does it mean to solve an inequality?

Back

To solve an inequality means to find all values of the variable that make the inequality true.

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all values that satisfy the inequality.

Front

What is an absolute value equation?

Back

An absolute value equation is an equation that contains an absolute value expression, which represents the distance of a number from zero on the number line.

Front

How do you solve an absolute value equation?

Back

To solve an absolute value equation, you set up two separate equations: one for the positive case and one for the negative case.

Front

What is the absolute value of a number?

Back

The absolute value of a number is its distance from zero on the number line, regardless of direction. It is always non-negative.

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What does the symbol '>' mean in inequalities?

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'>' means 'greater than'. For example, x > 5 means x is any number greater than 5.

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What does the symbol '<' mean in inequalities?

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'<'' means 'less than'. For example, x < 3 means x is any number less than 3.

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What does the symbol '≥' mean in inequalities?

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'≥' means 'greater than or equal to'. For example, x ≥ 4 means x is any number greater than or equal to 4.

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What does the symbol '≤' mean in inequalities?

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'≤' means 'less than or equal to'. For example, x ≤ 2 means x is any number less than or equal to 2.