Solutions to Linear Inequalities 8th 12/4

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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 (>, <, ≥, ≤) instead of an equal sign.

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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, often visualized as a shaded region on a graph.

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What is the significance of a dotted line in graphing linear inequalities?

Back

A dotted line indicates that points on the line are not included in the solution set, meaning the inequality is strict (using < or >).

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What does a solid line indicate in graphing linear inequalities?

Back

A solid line indicates that points on the line are included in the solution set, meaning the inequality is non-strict (using ≤ or ≥).

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

Back

To determine if a point is a solution, substitute the x and y values into the inequality. If the inequality holds true, the point is part of the solution set.

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What is the graphical representation of the inequality y < 2x + 3?

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The graph will show a dotted line for y = 2x + 3, with the area below the line shaded to represent all points where y is less than 2x + 3.

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What is the difference between a solution to an equation and a solution to an inequality?

Back

A solution to an equation is a specific point that makes the equation true, while a solution to an inequality includes a range of points that satisfy the inequality.

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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, whether it is included in the solution set depends on whether the line is solid (included) or dotted (not included).

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How can you test if a point is in the solution set of an inequality?

Back

You can test a point by substituting its coordinates into the inequality. If the resulting statement is true, the point is in the solution set.

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What is the role of the shaded region in the graph of a linear inequality?

Back

The shaded region represents all the possible solutions to the inequality, indicating where the inequality holds true.