Year 8: Solve inequalities in a single variable

What are Inequalities?

An inequality is a mathematical statement that shows that two expressions are not equal. It shows a relationship where one value is greater than, less than, greater than or equal to, or less than or equal to another.

Symbols

• > - Greater than
• < - Less than
• ≥ - Greater than or equal to
• ≤ - Less than or equal to

Steps to Solve Inequalities

1. Isolate the variable: Just like with equations, you need to get the variable by itself on one side of the inequality. Remember to do the same operation to both sides of the inequality to keep it balanced.
2. Change the sign: When you multiply or divide an inequality by a negative number, you *flip* the inequality sign.
3. Write the solution in interval notation: Inequalities are often written in interval notation.

Example

Solve: x + 2 > 5

1. Subtract 2 from both sides: x > 3
2. Write the solution in interval notation: (3, &infinity)

Important Note: Remember that if you multiply or divide an inequality by a negative number, you must flip the inequality sign.