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 -4 > -2 + x?

Back

To solve -4 > -2 + x, add 2 to both sides: -2 > x, which can be rewritten as x < -2.

Front

Which of the following is a solution for the inequality 12 > x + 1?

Back

A solution is x < 11, so -5 is a valid solution.

Front

What does a closed dot on a graph represent?

Back

A closed dot represents that the number is included in the solution set, used for ≤ and ≥ inequalities.

Front

What does an open dot on a graph represent?

Back

An open dot represents that the number is not included in the solution set, used for < and > inequalities.

Front

How do you graph the inequality 6 > x?

Back

Graph it with an open dot at 6 and shade to the left, indicating all numbers less than 6.