Linear Inequalities

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What is a linear inequality?

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A linear inequality is a mathematical statement that relates a linear expression to a value using inequality symbols (such as <, >, ≤, or ≥).

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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.

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

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Yes, if the inequality is ≤ or ≥; No, if the inequality is < or >.

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How do you write a linear inequality in standard form?

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A linear inequality in standard form is written as Ax + By < C, Ax + By > C, Ax + By ≤ C, or Ax + By ≥ C, where A, B, and C are constants.

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What is the significance of the y-intercept in a linear equation?

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The y-intercept is the point where the line crosses the y-axis, representing the value of y when x = 0.

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

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Substitute the coordinates of the point into the inequality. If the inequality holds true, the point is part of the solution set.

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What does the graph of a linear inequality look like?

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The graph of a linear inequality consists of a boundary line (solid for ≤ or ≥, dashed for < or >) and a shaded region representing the solution set.

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What is the difference between a solid line and a dashed line in the graph of a linear inequality?

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A solid line indicates that points on the line are included in the solution set (≤ or ≥), while a dashed line indicates they are not included (< or >).

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Front

What is the standard form of the inequality for making at least $240 from selling hot chocolate and apple cider?

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