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What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (e.g., <, >, ≤, ≥).

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What does the symbol '≤' mean in a linear 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.

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What does the symbol '≥' mean in a linear 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.

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How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a dashed line (for < or >) or a solid line (for ≤ or ≥). Then shade the region that satisfies the inequality.

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What is the solution set of a linear inequality?

Back

The solution set of a linear inequality is the set of all points (x, y) that satisfy the inequality.

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What does it mean if a point lies on the boundary line of a linear inequality?

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If a point lies on the boundary line, it is part of the solution set if the inequality includes equality (≤ or ≥).

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How can you determine if a point is in the solution set of a linear inequality?

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To determine if a point is in the solution set, substitute the point's coordinates into the inequality. If the inequality holds true, the point is in the solution set.

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

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

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What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

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How do you convert a linear equation to a linear inequality?

Back

To convert a linear equation to a linear inequality, replace the '=' sign with an inequality symbol (<, >, ≤, or ≥).