Linear Inequalities: Solution or Not?

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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 (>, <, ≥, ≤).

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What does the solution set of a linear inequality represent?

Back

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

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

Back

To determine if a point is in the solution set, substitute the x and y values of the point into the inequality and check if the statement is true.

Front

What is the significance of the boundary line in a linear inequality?

Back

The boundary line represents the points where the inequality changes from true to false. If the inequality is strict (>, <), the line is dashed; if it is inclusive (≥, ≤), the line is solid.

Front

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

Back

If a point lies above the boundary line, it is part of the solution set for inequalities of the form y > mx + b or y ≥ mx + b.

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

Back

If a point lies below the boundary line, it is part of the solution set for inequalities of the form y < mx + b or y ≤ mx + b.

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Back

No, substituting (3, 1) gives 1 ≤ -9 + 4, which is false.

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Back

Yes, substituting (2, 0) gives 0 ≤ -6 + 4, which is true.

Front

What is the graphical representation of a linear inequality?

Back

The graphical representation of a linear inequality is a shaded region on one side of the boundary line, indicating all the solution points.

Front

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

Back

If a point lies on the boundary line, it is included in the solution set if the inequality is inclusive (≥ or ≤).