Solving and Graphing Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols such as <, >, ≤, or ≥.

Front

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

Back

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

Front

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

Back

The symbol '<' means 'less than'. For example, x < 3 means x is less than 3.

Front

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

Back

The symbol '≥' means 'greater than or equal to'. For example, x ≥ 4 means x is greater than or equal to 4.

Front

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

Back

The symbol '≤' means 'less than or equal to'. For example, x ≤ 2 means x is less than or equal to 2.

Front

How do you solve the inequality 12 > x + 1?

Back

Subtract 1 from both sides: 12 - 1 > x, which simplifies to 11 > x or x < 11.

Front

What is the solution set for the inequality x > -6?

Back

The solution set includes all numbers greater than -6.

Front

When graphing the inequality x < 5, what type of dot is used?

Back

An open dot is used because the inequality does not include 5.

Front

When graphing the inequality x ≥ 3, what type of dot is used?

Back

A closed dot is used because the inequality includes 3.

Front

What is the solution to the inequality -4 > -2 + x?

Back

Add 2 to both sides: -4 + 2 > x, which simplifies to -2 > x or x < -2.