Real World Inequalities

Front

What is an inequality?

Back

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

Front

What does the symbol '>' mean in an inequality?

Back

The symbol '>' means 'greater than'. For example, 5 > 3 means that 5 is greater than 3.

Front

What does the symbol '<' mean in an inequality?

Back

The symbol '<' means 'less than'. For example, 2 < 4 means that 2 is less than 4.

Front

What does the symbol '≥' mean in an inequality?

Back

The symbol '≥' means 'greater than or equal to'. For example, 7 ≥ 7 means that 7 is greater than or equal to 7.

Front

What does the symbol '≤' mean in an inequality?

Back

The symbol '≤' means 'less than or equal to'. For example, 3 ≤ 5 means that 3 is less than or equal to 5.

Front

How do you solve a simple inequality like x + 3 < 7?

Back

To solve x + 3 < 7, subtract 3 from both sides: x < 4.

Front

What is a solution set in the context of inequalities?

Back

A solution set is the set of all values that satisfy the inequality. For example, the solution set for x < 4 is all numbers less than 4.

Front

How can you represent an inequality on a number line?

Back

To represent 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 a compound inequality?

Back

A compound inequality combines two inequalities, such as a < x < b, which means x is greater than a and less than b.

Front

How do you graph a compound inequality like 2 < x ≤ 5?

Back

Graph 2 with an open circle and 5 with a closed circle, then shade the region between them.