Linear Inequalities and Systems of Linear Inequalities Check

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What is a linear inequality?

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A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (>, <, ≥, ≤). It represents a region of solutions on a graph.

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What does the solution set of a linear inequality represent?

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The solution set of a linear inequality represents all the points (x, y) that satisfy the inequality, forming a region on the coordinate plane.

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How do you graph a linear inequality?

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To graph a linear inequality, first graph the corresponding linear equation as a boundary line. Use a dashed line for < or > (not included) and a solid line for ≤ or ≥ (included). Then shade the region that satisfies the inequality.

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What is the difference between a linear equation and a linear inequality?

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A linear equation has a single solution (a line), while a linear inequality has multiple solutions (a region) that satisfy the inequality.

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What does it mean for an inequality to have multiple solutions?

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It means that there are infinitely many values that satisfy the inequality, forming a continuous range of solutions.

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

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The boundary line separates the coordinate plane into two regions: one that satisfies the inequality and one that does not.

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

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

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What is the standard form of a linear inequality?

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

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The symbol '≥' indicates that the value on the left is greater than or equal to the value on the right, meaning the boundary line is included in the solution set.

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How do you write an inequality for a real-world situation?

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