Solving Inequalities and Absolute Value Equations

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions, showing 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

How do you graph an inequality on a number line?

Back

To graph an inequality on a number line, use an open circle for < or > and a closed circle for ≤ or ≥, then shade the appropriate direction.

Front

What is absolute value?

Back

Absolute value is the distance of a number from zero on the number line, regardless of direction.

Front

How do you solve an absolute value equation?

Back

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

Front

What is interval notation?

Back

Interval notation is a way of writing subsets of the real number line using intervals, such as (a, b) or [a, b].

Front

What does the notation (a, b) mean?

Back

The notation (a, b) represents an open interval, meaning it includes all numbers between a and b, but not a and b themselves.

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What does the notation [a, b] mean?

Back

The notation [a, b] represents a closed interval, meaning it includes all numbers between a and b, including a and b.

Front

What is a quadratic inequality?

Back

A quadratic inequality is an inequality that involves a quadratic expression, typically in the form ax² + bx + c < 0 or ax² + bx + c > 0.