Solving Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, greater than or equal to, or less than or equal to the other.

Front

What symbols are used to represent inequalities?

Back

The symbols used to represent inequalities are: > (greater than), < (less than), ≥ (greater than or equal to), and ≤ (less than or equal to).

Front

How do you solve a simple linear inequality?

Back

To solve a simple linear inequality, isolate the variable on one side of the inequality sign using inverse operations, similar to solving an equation.

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 reverse the inequality sign.

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

How can you graph an inequality on a number line?

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To graph an inequality on a number line, use an open circle for < or > and a closed circle for ≤ or ≥, then shade the region that represents the solution set.

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What is a compound inequality?

Back

A compound inequality is an inequality that combines two or more inequalities, often connected by 'and' or 'or'.

Front

How do you solve a compound inequality?

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To solve a compound inequality, solve each inequality separately and then find the intersection (for 'and') or the union (for 'or') of the solution sets.

Front

What is the difference between strict and non-strict inequalities?

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Strict inequalities (<, >) do not include the endpoints, while non-strict inequalities (≤, ≥) include the endpoints.

Front

What is an absolute value inequality?

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An absolute value inequality is an inequality that contains an absolute value expression, which can be solved by considering two cases: one for the positive and one for the negative scenario.