Solving and Graphing Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using inequality symbols (such as <, >, ≤, ≥) to show that one expression is less than, greater than, or equal to another.

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 interval notation?

Back

Interval notation is a way of writing subsets of the real number line using intervals, which can be open or closed.

Front

What does the notation (a, b) represent?

Back

The notation (a, b) represents an open interval, meaning that a and b are not included in the set.

Front

What does the notation [a, b] represent?

Back

The notation [a, b] represents a closed interval, meaning that a and b are included in the set.

Front

What happens to the inequality sign when you multiply or divide by a negative number?

Back

When you multiply or divide both sides of an inequality by a negative number, you must flip the inequality sign.

Front

How do you graph the inequality x < 3?

Back

To graph x < 3, draw a number line, place an open circle on 3, and shade to the left to indicate all numbers less than 3.

Front

How do you graph the inequality x ≥ -2?

Back

To graph x ≥ -2, draw a number line, place a closed circle on -2, and shade to the right to indicate all numbers greater than or equal to -2.

Front

What is the largest integer that satisfies the inequality 7(x + 3) - 5x < 13?

Back

The largest integer that satisfies the inequality is -5.