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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 (>, <, ≥, ≤). It represents a region of the coordinate plane.

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What does the symbol '>' indicate in a linear inequality?

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The symbol '>' indicates that the values of the variable are greater than the value on the other side of the inequality.

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What does the symbol '<' indicate in a linear inequality?

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The symbol '<' indicates that the values of the variable are less than the value on the other side of the inequality.

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What does the symbol '≥' indicate in a linear inequality?

Back

The symbol '≥' indicates that the values of the variable are greater than or equal to the value on the other side of the inequality.

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What does the symbol '≤' indicate in a linear inequality?

Back

The symbol '≤' indicates that the values of the variable are less than or equal to the value on the other side of the inequality.

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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 dashed line (for < or >) or a solid line (for ≤ or ≥). Then shade the region that satisfies the inequality.

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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, represented graphically as a shaded region on the coordinate plane.

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

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To determine if a point is in the solution set, substitute the coordinates of the point into the inequality. If the inequality holds true, the point is in the solution set.

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

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

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What is the slope-intercept form of a linear equation?

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The slope-intercept form of a linear equation is given by the formula y = mx + b, where m is the slope and b is the y-intercept.