Solving Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that relates a linear expression to a value using inequality symbols (such as <, >, ≤, or ≥) instead of an equal sign.

Front

How do you solve a linear inequality?

Back

To solve a linear inequality, isolate the variable on one side of the inequality using inverse operations, similar to solving an equation, while remembering to reverse the inequality sign if you multiply or divide by a negative number.

Front

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

Back

The symbol '≤' means 'less than or equal to', indicating that the value on the left can be less than or equal to the value on the right.

Front

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

Back

The symbol '≥' means 'greater than or equal to', indicating that the value on the left can be greater than or equal to the value on the right.

Front

How do you graph a linear inequality on a number line?

Back

To graph a linear inequality on a number line, use an open circle for < or > (not including the endpoint) and a closed circle for ≤ or ≥ (including the endpoint). Shade the region that satisfies the inequality.

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all values that make the inequality true, often represented graphically or in interval notation.

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

How do you translate a verbal statement into a linear inequality?

Back

To translate a verbal statement into a linear inequality, identify the key terms (like 'at most', 'at least', 'more than', 'less than') and assign variables to the quantities involved.

Front

What does 'at most' mean in terms of inequalities?

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'At most' indicates a maximum limit, which translates to a 'less than or equal to' inequality (≤).

Front

What does 'at least' mean in terms of inequalities?

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'At least' indicates a minimum limit, which translates to a 'greater than or equal to' inequality (≥).