Is the Point a Solution?

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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 it mean for a point to be a solution to a linear inequality?

Back

A point is a solution to a linear inequality if its coordinates satisfy the inequality when substituted into the expression.

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What is the solution set of a linear inequality?

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

Tags

CCSS.HSA.REI.D.12

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Are points on the boundary line of a linear inequality included in the solution set?

Back

Points on the boundary line are included if the inequality is '≤' or '≥', but not if it is '<' or '>'.

Tags

CCSS.HSA.REI.D.12

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How do you determine if a point is a solution to an inequality?

Back

Substitute the x and y coordinates of the point into the inequality and check if the statement is true.

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What is the difference between a strict inequality and a non-strict inequality?

Back

A strict inequality (< or >) does not include the boundary, while a non-strict inequality (≤ or ≥) includes the boundary.

Tags

CCSS.6.EE.B.8

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What does the term 'solution set' refer to?

Back

The solution set refers to all the points that satisfy a given inequality or equation.

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What is the graphical representation of a linear inequality?

Back

The graphical representation is a shaded region on one side of the boundary line, indicating all the solutions.

Tags

CCSS.HSA.REI.D.12

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What does it mean if a point is 'sometimes' a solution?

Back

It means that the point may satisfy the inequality under certain conditions or for specific values.